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Paper Citation Record · LEDGER

Short Paths in the Planar Graph Product Structure Theorem

As of 12 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 0 inbound Pith citation observations for arXiv:2502.01927.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2502.01927 v1

Coverage vector

measured 60 of 60 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T14:12:32.949264Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

60 of 60 outbound references displayed

  • verified exact3
  • verified fuzzy33
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f71918a0-a7cf-447e-8f93-811c9da71e26 · outbound

This paper cites Characterization and recognition of partial 3-trees.

Short Paths in the Planar Graph Product Structure Theorem Characterization and recognition of partial 3-trees

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.584387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.736827Z digest=sha256:c99794f3f131a64f976be8bca3ba1d57b546d5825c8068afca2be6e09b991143

Observation c51718db-631d-4a1c-b5d7-888c04b14037 · outbound

This paper cites Bekos and Luca Grilli.

Short Paths in the Planar Graph Product Structure Theorem Bekos and Luca Grilli

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.573639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.741248Z digest=sha256:c4fca72b685e3da235e25354170eddd521b28578d119b4a8ba62db230b503a0a

Observation 5ac4cf7b-510d-4d1c-a558-933c0834bf4d · outbound

This paper cites Bekos, Giordano Da Lozzo, Petr Hlinený, and Michael Kaufmann.

Short Paths in the Planar Graph Product Structure Theorem Bekos, Giordano Da Lozzo, Petr Hlinený, and Michael Kaufmann

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.562213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.745183Z digest=sha256:053e7bbd5f9900e0bdf82f8fac90f0901fe0a2c55ca79a7ee898bbfd92a31356

Observation d7ac67e8-bd77-4b75-baf7-d24bff49cabc · outbound

This paper cites Drawing planar 3-trees with given face areas.

Short Paths in the Planar Graph Product Structure Theorem Drawing planar 3-trees with given face areas

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.748964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.748964Z digest=sha256:9fc22c22075b6bc73cf33c28c40b99dfbb99916a16c5d5b82dfb8d7d298dad05

Observation 939d2b5d-2d13-4bfc-9b3f-f07bd12ffbad · outbound

This paper cites Bodlaender.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.542963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.752914Z digest=sha256:c5738825e5f6c9cdb23ea327763fa1afb8e95d1ef5bad9797533430dd31a55fe

Observation fcb5ddda-e49d-412d-b112-ef67b61d5169 · outbound

This paper cites Bodlaender.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.532166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.756728Z digest=sha256:2f4d367e091b05173fd56e1da5950f6f1b8789d97560a6f1e616834664b288e1

Observation 5143fc20-ee43-48a8-bd0b-1a83369f352a · outbound

This paper cites Bodlaender and Joost Engelfriet.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender and Joost Engelfriet

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.521811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.760520Z digest=sha256:f0a7ef1ecd83d5f88a25acc1667f0a220c14fa8bc183ccbaebf2dd43a1022af3

Observation 72dcd3c8-68ec-4287-9f2f-7af741f6e66d · outbound

This paper cites Bodlaender, Carla Groenland, and Hugo Jacob.

Short Paths in the Planar Graph Product Structure Theorem Bodlaender, Carla Groenland, and Hugo Jacob

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.511143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.763701Z digest=sha256:1bc8769fe015f9e0e8780cd0419c6451cc70d84ea640a92cf7c0c94718dd1dba

Observation 7d9f29bd-ab3d-40ab-a62b-4c2c9eb3c651 · outbound

This paper cites Shorter labeling schemes for planar graphs.

Short Paths in the Planar Graph Product Structure Theorem Shorter labeling schemes for planar graphs

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.499797Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.767097Z digest=sha256:4ef3f729e7673469b2f30a912004f35b218f827e782b7e97b258b18c192af0ea

Observation f7864373-8b61-493d-a01d-9b9d079437e5 · outbound

This paper cites Pruessmann, Anusch Taraz, and Andreas Würfl.

Short Paths in the Planar Graph Product Structure Theorem Pruessmann, Anusch Taraz, and Andreas Würfl

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.489623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.770118Z digest=sha256:8bf8f781dc0922093a9a9fab7f8e3f5fca58dad5c4194415af938e71d1abbaa9

Observation 4b7815b4-6bfc-4ff6-b115-2dc881d13ba6 · outbound

This paper cites Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Pascal Gollin, Kevin Hendrey, Robert Hickingbotham, Tony Huynh, Freddie Illingworth, Youri Tamitegama, Jane Tan, and Da vid R

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.478720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.774372Z digest=sha256:9e0df0304cccc2e04d13fe0de62e1bacd57a12a00b733fcc153b9bf07b8004f3

Observation ffc35aab-c05f-4553-a1b3-3020bcae9557 · outbound

This paper cites Apollonian ball packings and stacked polytopes.Discrete Comput.

Short Paths in the Planar Graph Product Structure Theorem Apollonian ball packings and stacked polytopes.Discrete Comput

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.468242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.777436Z digest=sha256:9a44b15bcd3c72325982972b500cb1456d79268711bad67253c3a35d8b59f1a6

Observation eadffa25-3b2a-44ef-a7d4-63ee52986baa · outbound

This paper cites The thickness of fan-planar graphs is at most three.

Short Paths in the Planar Graph Product Structure Theorem The thickness of fan-planar graphs is at most three

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.457922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.780592Z digest=sha256:58ccdf59669cfeb0199ab813c842aed03d044199903d6db476e33009af139cc8

Observation bb67acd3-4ef4-441f-880c-a9bb8bea82a2 · outbound

This paper cites Some results on tree decomposition of graphs.J.

Short Paths in the Planar Graph Product Structure Theorem Some results on tree decomposition of graphs.J

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.784718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.784718Z digest=sha256:f5a9f03c3f3dd3dcf8765e02c3406121a45a3a43400ccd138b5532c5612f5bb5

Observation c8b9e675-a5f1-499a-ae7f-286290a15552 · outbound

This paper cites On tree-partitions of graphs.Discrete Math., 149(1– 3):45–58, 1996.

Short Paths in the Planar Graph Product Structure Theorem On tree-partitions of graphs.Discrete Math., 149(1– 3):45–58, 1996

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.441255Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.788369Z digest=sha256:4c1c038a97c4556bc4c29e34abce2ecfd8aa5053e31e691af7213ce9d504d4f4

Observation 49a54fbe-3d8a-4612-a267-29a8962981eb · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.430958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.792220Z digest=sha256:18ab4454f519925c05e7ac3fa5b3ac1a82acd772b4192a46fa3d7293c8192d83

Observation a58e5913-b432-40ff-ab57-c21c4b33c4fc · outbound

This paper cites Seweryn, and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Seweryn, and Da vid R

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.420739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.795826Z digest=sha256:6c18687ecef5dbe56b27b9eef9a6e99f32d88a1b83c0079ac675aedbaa0c6991

Observation b5ff7e97-fba7-423a-ab94-24d0f3d78942 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.409251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.799232Z digest=sha256:1438e195faa153fc11a4491ad984858db926d58a25e894d0d927195e1391284f

Observation ed019191-15d1-4ac8-9488-f9806c58f0e4 · outbound

This paper cites Improved bounds for centered colorings.Adv.

Short Paths in the Planar Graph Product Structure Theorem Improved bounds for centered colorings.Adv

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.398748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.802781Z digest=sha256:4847d8f9c9f870b03b9dec12ba3e38dd13d083ed4b70e33f5204f4c79eb6b494

Observation 12095158-f9b9-4f93-ae31-1686b7eaf1c1 · outbound

This paper cites Size-Ramsey numbers of structurally sparse graphs.

Short Paths in the Planar Graph Product Structure Theorem Size-Ramsey numbers of structurally sparse graphs

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.806261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.806261Z digest=sha256:7bdf01f776f55ba2a204bad347f3ef3f05eb433bee552e013697d30c71eb3137

Observation 56aa0325-141a-459e-950f-a63e84803a93 · outbound

This paper cites Adjacency labelling for planar graphs (and beyond).J.

Short Paths in the Planar Graph Product Structure Theorem Adjacency labelling for planar graphs (and beyond).J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.387893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.810178Z digest=sha256:083ce92b46b29bf7233a966f71ea301e36a0d6528fa7a9805c37824b18aac229

Observation f6c622df-fc00-4b7e-8051-037018d5887b · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.377561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.813424Z digest=sha256:f69c50591278c4bef0772a386db0494a9ad29b0440b9682bb923e5edf924301e

Observation 5a5f893f-d780-4feb-8ec8-9e40b73a2afd · outbound

This paper cites The grid-minor theorem revisited.

Short Paths in the Planar Graph Product Structure Theorem The grid-minor theorem revisited

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.817196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.817196Z digest=sha256:76b82e01bd1e4fb8189a28496474162c8ecfdee79f3c67d33da16b50da44724d

Observation 1d786411-04bf-44a2-8715-fa8194961578 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.366291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.821169Z digest=sha256:c3b6ac6cd553707244d42fa3eb21f698feeea0b627e045b5c845fb8c081b3a51

Observation 13c88c4a-d05e-4fa1-904f-54c91fea6bf9 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.355685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.824315Z digest=sha256:6cb0a8b6011759fb3fb1e046b1e5daafe1da761fc3828b14539089c068acd600

Observation a621474d-992c-425f-8a79-598098a2f505 · outbound

This paper cites Layered Separators in Minor-Closed Graph Classes with Applications.

Short Paths in the Planar Graph Product Structure Theorem Layered Separators in Minor-Closed Graph Classes with Applications

Reference 26

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.827700Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.827700Z digest=sha256:8d16b51b2a61e14d222af9ff34b55c8741000a20ab196af1009e687dbb8ff6aa

Observation 98b84c24-5577-442e-a6a1-26abe1772690 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.344353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.831494Z digest=sha256:04c5d92ac04a158124751a02689f7f26c4d81415d3ce0176b20e4c8a9a73c8cd

Observation 2d54a038-107c-4b82-aac6-c7dc62273857 · outbound

This paper cites Grid Minors and Products.

Short Paths in the Planar Graph Product Structure Theorem Grid Minors and Products

Reference 28

Resolution
metadata mismatch
local_arxiv, observed 2026-08-09T14:12:33.058193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.834751Z digest=sha256:ccb5ff51f79c24f16158a88e383d26641053d754acf51d520c04be7d9fc6ae2d

Observation bd6f5483-ce8e-432f-b308-9752ca2c497b · outbound

This paper cites On comparable box dimension.

Short Paths in the Planar Graph Product Structure Theorem On comparable box dimension

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.333980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.838362Z digest=sha256:2887373849e7d272e61764a1fdddabeb3b93f2882f2f61956fcb9127c6615b10

Observation 82d203d2-1c28-4fc9-aeb0-9e2aeb7f1d76 · outbound

This paper cites On fractional fragility rates of graph classes.

Short Paths in the Planar Graph Product Structure Theorem On fractional fragility rates of graph classes

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.323669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.841671Z digest=sha256:76b1d07804b1e89823e47329eb20a12e6ca599cb6c2d2ebf87750f355327cfd0

Observation 4542b8f9-70b5-4db9-8d5f-c57384e53faf · outbound

This paper cites Quotient tree partitioning of undirected graphs.BIT, 26(2):148–155, 1986.

Short Paths in the Planar Graph Product Structure Theorem Quotient tree partitioning of undirected graphs.BIT, 26(2):148–155, 1986

Reference 31

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.844997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.844997Z digest=sha256:1596bb0d7eb4b3ea5d0830d1a58241b5492137025f32cb330002ee16acc9ea4c

Observation a463c5c4-ebe1-4242-bd0e-e2e7d43bd883 · outbound

This paper cites Subgraph isomorphism in planar graphs and related problems.

Short Paths in the Planar Graph Product Structure Theorem Subgraph isomorphism in planar graphs and related problems

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.307576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.848566Z digest=sha256:72746237abd5dbe2cb384856d42e655caf385efef23f1e009ca497befdc59961

Observation abb18c7c-9f69-4d76-86fa-acdad2f060b4 · outbound

This paper cites Sparse universal graphs for planarity.J.

Short Paths in the Planar Graph Product Structure Theorem Sparse universal graphs for planarity.J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.297510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.852552Z digest=sha256:08ecf6151fbe954eaaf068354c1a5c1c4fd99def2bcb394ce55b4798e3f20137

Observation 1d981d9d-c635-44df-bfc0-c0a1fbaffdb4 · outbound

This paper cites Tsourakakis.

Short Paths in the Planar Graph Product Structure Theorem Tsourakakis

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.286449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.856040Z digest=sha256:8d5f75d9df258122aff85fcb0163aeab9077584822a077ce3ca4140f4054ef3c

Observation 20daa068-dcad-4197-acc2-60ade515c299 · outbound

This paper cites 3D-grids are not transducible from planar graphs.

Short Paths in the Planar Graph Product Structure Theorem 3D-grids are not transducible from planar graphs

Reference 35

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.859835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.859835Z digest=sha256:65c959b3ca1b465731318d7861e5cdcf3c631adef631a282c805825b97360397

Observation e79d201d-11a0-4fc1-afd6-d6212e942f11 · outbound

This paper cites Simpler adjacency labeling for planar graphs with B-trees.

Short Paths in the Planar Graph Product Structure Theorem Simpler adjacency labeling for planar graphs with B-trees

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.276310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.863822Z digest=sha256:7f1ca69c89df437eb51ebfc74e2dd7e6386ac5a288db08603b0fb097ef1b22d5

Observation aaa38288-a7d5-4c3f-bb9b-605e9bd33d0b · outbound

This paper cites Tree-partitions of infinite graphs.Discrete Math., 97:203–217, 1991.

Short Paths in the Planar Graph Product Structure Theorem Tree-partitions of infinite graphs.Discrete Math., 97:203–217, 1991

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.867194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.867194Z digest=sha256:f2eeacf1d64cc6607e50216643a0aa56eb6635bff738afb162e871e2a26c01e7

Observation 9c7f1ee5-6d16-46a3-8795-c17ad451dc0a · outbound

This paper cites Har vey and Da vid R.

Short Paths in the Planar Graph Product Structure Theorem Har vey and Da vid R

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.259224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.870346Z digest=sha256:bdb2a8b9e9260cb995d9836987c2dd2e822842794d96336ba075854e5095f7f1

Observation 39810498-6eb4-45f9-b2b3-1793c5531909 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.249523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.873767Z digest=sha256:88a2d47b8378a9eed1952ece4220387c69080674be3dc07b3e55f3aabed87e3a

Observation 3f406323-5f4a-4f19-a4f4-71daf75628ec · outbound

This paper cites H-clique-width and a hereditary analogue of product structure.

Short Paths in the Planar Graph Product Structure Theorem H-clique-width and a hereditary analogue of product structure

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.239407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.876973Z digest=sha256:ccd24af1bad53060ede9e76493c573f3d5d3827e8018b17254a223cbf2ea5cc3

Observation 13f05797-34c6-44e2-8c6c-8321dae86f37 · outbound

This paper cites Transductions of Graph Classes Admitting Product Structure.

Short Paths in the Planar Graph Product Structure Theorem Transductions of Graph Classes Admitting Product Structure

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.881181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.881181Z digest=sha256:8090611ba684aea52c80b5d28ac74093fbe4b24fcad1200818f09a061e2b91f7

Observation 721133ca-65a9-4ec9-b443-d94f638e55db · outbound

This paper cites Universality in minor-closed graph classes.

Short Paths in the Planar Graph Product Structure Theorem Universality in minor-closed graph classes

Reference 42

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:33.025914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.885752Z digest=sha256:c899c5915ffe1b533fd29717e70fcacfb1ac0fd944aa56d38bc10bad8781eb21

Observation e8ce47b2-6196-4ac0-aaaa-d543dc06d052 · outbound

This paper cites Product structure of graphs with an excluded minor.

Short Paths in the Planar Graph Product Structure Theorem Product structure of graphs with an excluded minor

Reference 43

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:33.011804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.889428Z digest=sha256:98a5389bf7cd29d3f6bede63f810f863f1626f03a4721b4acae6665004e626b7

Observation d538f02a-2c80-4d5a-b9cf-84cdc1eee677 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.229227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.893680Z digest=sha256:78747fd453974e711cae213346627bee422b15777e57b361796db71c273de33f

Observation 6c42231b-d842-46ab-94e9-8ae059c0da42 · outbound

This paper cites Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs.

Short Paths in the Planar Graph Product Structure Theorem Bounding twin-width for bounded-treewidth graphs, planar graphs, and bipartite graphs

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.219012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.897047Z digest=sha256:8d30e987eee1a6640381d2b91736fb470092347dd4cc8e0a3aaba386b36922be

Observation bdbc4a97-4a19-4c21-9073-545c446ee6c2 · outbound

This paper cites The density of fan-planar graphs.Electron.

Short Paths in the Planar Graph Product Structure Theorem The density of fan-planar graphs.Electron

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.208180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.900400Z digest=sha256:25697f3aa839e86ee6ff2988775fb8d04d030f41e448186d496abf71a4022fba

Observation 8887926b-8369-46cd-97c3-72dbb67e6993 · outbound

This paper cites Simple treewidth.

Short Paths in the Planar Graph Product Structure Theorem Simple treewidth

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.197580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.903787Z digest=sha256:cb3e330c1087c8aeef94ebb54bd6f8ce47ed885a8c688227dcc5b29224426d85

Observation f0f89812-c2b4-4717-9a18-962be72ed0b8 · outbound

This paper cites A note on planar partial 3-trees.

Short Paths in the Planar Graph Product Structure Theorem A note on planar partial 3-trees

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.907455Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.907455Z digest=sha256:1d3b4c359a9b47d3a8c47db4ae62c1bc4854c3ec349881d89a00a97b2b8f4382

Observation 2e8fb341-3796-42dc-88fd-99ef873b8812 · outbound

This paper cites Twin-width of graphs on surfaces.

Short Paths in the Planar Graph Product Structure Theorem Twin-width of graphs on surfaces

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.187733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.911195Z digest=sha256:d48620bea5052255f2f97e201100e95617bec1c456fb12e73968ae2105e77afe

Observation c3081497-fe0e-45f9-a9c7-af01c4f95d6b · outbound

This paper cites Paciornik.

Short Paths in the Planar Graph Product Structure Theorem Paciornik

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.177179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.914500Z digest=sha256:31953778c671be7fca58bb3cdca200ee86960cabe0e08c2deee7095d3311d890

Observation d28915ec-0260-48f6-8613-23b50db74f8d · outbound

This paper cites Graphs drawn with few crossings per edge.Combinatorica, 17(3):427–439, 1997.

Short Paths in the Planar Graph Product Structure Theorem Graphs drawn with few crossings per edge.Combinatorica, 17(3):427–439, 1997

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.166808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.918522Z digest=sha256:799de9ea916f6a317abd1a649d3bedfb8ca8274394b01f104df2cb99c9a9c97a

Observation 1196c5e5-ac31-466a-8b6b-bda358dfaa1a · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 52

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.921749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.921749Z digest=sha256:1efd5ce8bcd4be569dc129cf5328d870021ccadd38491ef92bcc724b058e98d7

Observation e4b8ae72-a0f7-4f45-ba90-87b26eb61f5c · outbound

This paper cites Tree-partite graphs and the complexity of algorithms.

Short Paths in the Planar Graph Product Structure Theorem Tree-partite graphs and the complexity of algorithms

Reference 53

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.925162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.925162Z digest=sha256:f299815741f8f3e2e7665695f05ab9df69417b8cd47c993e0899b09bcbd4b895

Observation 84a71c30-aff1-4166-b72f-205ab2fb0030 · outbound

This paper cites Graph searching and a min-max theorem for tree-width.

Short Paths in the Planar Graph Product Structure Theorem Graph searching and a min-max theorem for tree-width

Reference 54

Resolution
unresolved
no resolver link, observed 2026-08-09T14:12:32.928609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-09T14:12:32.928609Z digest=sha256:6529cbdf1289023eea76eef9c590c571f09cb34257ded80806842be7facaa392

Observation 489a027c-0e3f-4b33-8be2-0deadf29adc4 · outbound

This paper cites New representation results for planar graphs.

Short Paths in the Planar Graph Product Structure Theorem New representation results for planar graphs

Reference 55

Resolution
verified exact
local_arxiv, observed 2026-08-09T14:12:32.985770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.931986Z digest=sha256:62e6900ba0e0fb184e64ac22cc557fc394cccf2be88084903d977fa2777cdc35

Observation 543a19be-2233-4dad-92ba-db2f42c6c9bf · outbound

This paper cites Wood, and Wendy Yi.

Short Paths in the Planar Graph Product Structure Theorem Wood, and Wendy Yi

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.137279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.935576Z digest=sha256:be65ea99733ee58688eddf5aeafdf7ee4b148ba069d5a15dc5cc0cf4eca7524c

Observation bbf934f6-437a-4701-ba55-f2c986b67574 · outbound

This paper cites Geometrie der lage.

Short Paths in the Planar Graph Product Structure Theorem Geometrie der lage

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.127104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.938775Z digest=sha256:c2da70f56c155cb5a73f5e836db1fa4ca6d0d81f6a606912a22afa187050f6dd

Observation de8ab704-2cee-4960-b73e-2d2f34338a59 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.116833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.942247Z digest=sha256:d56e451ace9aec8fccd31fb4ddd45f28b733589e314955d8ff8ef1aea3b1577e

Observation 3b70dce9-fde0-448f-b411-1c30ea667c84 · outbound

This paper cites an unresolved cited work.

Short Paths in the Planar Graph Product Structure Theorem Unresolved cited work

Reference 59

Resolution
unresolved
raw_fallback, observed 2026-08-09T14:12:33.106686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.945858Z digest=sha256:985e4522926163d40b9f835a885fda946aef5e4e77f9157ac0107b53d20041c6

Observation 723b3ed3-4429-4738-a629-134ddff02ee6 · outbound

This paper cites Stacked treewidth and the Colin de Verdiére number.

Short Paths in the Planar Graph Product Structure Theorem Stacked treewidth and the Colin de Verdiére number

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-09T14:12:33.096725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-09T14:12:32.949264Z digest=sha256:6b5687e6236ca66f1325ce7be691fba0cd80acdc64ea4dce855063d5086291dd

Pith citing papers

No inbound Pith citation observations are available.