Paper Citation Record · LEDGER

3-Colouring Planar Graphs

As of 13 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 1 inbound Pith citation observation for arXiv:2507.03163.

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

pith.paper-citation-record.v1
2507.03163 v2

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:40:20.093036Z

measured 46 of 46 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T05:07:02.479725Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact7
verified fuzzy17
unresolved21
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a2eefb4f-f9d7-4c80-ab78-e5b43f0bab2c · outbound

This paper cites A separator theorem for nonplanar graphs.

3-Colouring Planar Graphs A separator theorem for nonplanar graphs

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:15.170861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d006b4e1-afb1-4fa8-bfb1-bfbadee4db44 · outbound

This paper cites Planar separators.SIAM J.

3-Colouring Planar Graphs Planar separators.SIAM J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:26.598087Z

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.

Observation b43d5378-0da6-48f1-827c-993d200f18c6 · outbound

This paper cites Every planar map is four colorable, vol.

3-Colouring Planar Graphs Every planar map is four colorable, vol

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:15.357462Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00285804-493a-42bf-aeda-600b143b179f · outbound

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

3-Colouring Planar Graphs Drawing planar 3-trees with given face areas

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:26.438393Z

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.

Observation 47d88b74-0860-435e-9a2d-2946d8f4922c · outbound

This paper cites Bodlaender.

3-Colouring Planar Graphs Bodlaender

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:15.587176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0375176b-8c6b-429d-8fef-29d1c5503370 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 6

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:40:21.557217Z

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.

Observation 8d189dcb-2ccf-494c-b275-cad30428a2bd · outbound

This paper cites Weak diameter choosability of graphs with an excluded minor.

3-Colouring Planar Graphs Weak diameter choosability of graphs with an excluded minor

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:26.266779Z

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.

Observation 0b7d7a90-5c65-4e13-8985-e22820f29e69 · outbound

This paper cites Graph theory, vol.

3-Colouring Planar Graphs Graph theory, vol

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:26.087417Z

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.

Observation 0f47c983-887f-40dc-b5a1-c5681ad925e2 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:25.862288Z

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.

Observation cf77d2a9-79d8-4e26-88c7-d4429eb2189f · outbound

This paper cites Proof of the Clustered Hadwiger Conjecture.

3-Colouring Planar Graphs Proof of the Clustered Hadwiger Conjecture

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:21.310809Z

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.

Observation 5efb8691-d3d5-475b-8472-01c1c8e9e9d5 · outbound

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

3-Colouring Planar Graphs Layered Separators in Minor-Closed Graph Classes with Applications

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:16.108147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3809667-95a3-4465-a328-972f62e184fe · outbound

This paper cites Islands in minor-closed classes. I. Bounded treewidth and separators.

3-Colouring Planar Graphs Islands in minor-closed classes. I. Bounded treewidth and separators

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:21.155976Z

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.

Observation ab68856f-018f-4fca-aebb-bfc4142a3b0e · outbound

This paper cites Treewidth of graphs with balanced separations.J.

3-Colouring Planar Graphs Treewidth of graphs with balanced separations.J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:16.371584Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ce2250c-3601-476e-8c32-384504b2e210 · outbound

This paper cites Product structure of graph classes with strongly sublinear separators.

3-Colouring Planar Graphs Product structure of graph classes with strongly sublinear separators

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:16.543292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 673182eb-a544-42f1-a882-27730206a144 · outbound

This paper cites A relative of Hadwiger’s conjecture.SIAM J.

3-Colouring Planar Graphs A relative of Hadwiger’s conjecture.SIAM J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:25.678721Z

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.

Observation f35cc33b-ac14-4863-aa52-71867b5b110e · outbound

This paper cites Harvey and David R.

3-Colouring Planar Graphs Harvey and David R

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:16.766297Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9adf8a7-beff-4d98-b3f5-04a25a25b079 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:25.552828Z

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.

Observation f9891273-f8b9-4d36-9a81-93a03ee03c95 · outbound

This paper cites Clustered Colouring of Odd-$H$-Minor-Free Graphs.

3-Colouring Planar Graphs Clustered Colouring of Odd-$H$-Minor-Free Graphs

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:21.016521Z

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.

Observation e6a86daf-7192-47da-a1ff-ef182ae5cb9c · outbound

This paper cites Separation Number and Treewidth, Revisited.

3-Colouring Planar Graphs Separation Number and Treewidth, Revisited

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:17.086104Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 794f82e1-4750-4ba4-b55e-a3ffb951fc81 · outbound

This paper cites Improper coloring of graphs with no odd clique minor.

3-Colouring Planar Graphs Improper coloring of graphs with no odd clique minor

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:25.399911Z

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.

Observation aa136a19-3b9e-425e-8ad0-d4f1ded45a7f · outbound

This paper cites A weakening of the odd Hadwiger’s conjecture.Combin.

3-Colouring Planar Graphs A weakening of the odd Hadwiger’s conjecture.Combin

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:25.180019Z

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.

Observation b146074b-9cbe-4189-bf42-5efa4ec2429a · outbound

This paper cites A relaxed Hadwiger’s conjecture for list colorings.

3-Colouring Planar Graphs A relaxed Hadwiger’s conjecture for list colorings

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:24.988387Z

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.

Observation 61d3e13e-3bc6-453d-8420-394a582903b7 · outbound

This paper cites Kleinberg, Rajeev Motwani, Prabhakar Raghavan, and Suresh Venkata- subramanian.

3-Colouring Planar Graphs Kleinberg, Rajeev Motwani, Prabhakar Raghavan, and Suresh Venkata- subramanian

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:24.796651Z

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.

Observation 50f26f50-bcb4-4863-ad68-462b8d87c3b4 · outbound

This paper cites Graph colouring with no large monochromatic components.Combin.

3-Colouring Planar Graphs Graph colouring with no large monochromatic components.Combin

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:24.504284Z

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.

Observation 909018b0-f289-4770-b2c6-431f129351b4 · outbound

This paper cites Lipton and Robert E.

3-Colouring Planar Graphs Lipton and Robert E

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:24.323309Z

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.

Observation ea523712-9083-4139-8fcc-9dbc86f83ca5 · outbound

This paper cites Lipton and Robert E.

3-Colouring Planar Graphs Lipton and Robert E

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:24.097732Z

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.

Observation 182fd064-30b4-4eae-9a54-764347af9467 · outbound

This paper cites Defective coloring is perfect for minors.Combinatorica, 44:467–507, 2024.

3-Colouring Planar Graphs Defective coloring is perfect for minors.Combinatorica, 44:467–507, 2024

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:23.859926Z

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.

Observation 18cd43a0-7387-4b74-8b53-af3cff9ddcbd · outbound

This paper cites PartitioningH-minor free graphs into three subgraphs with no large components.J.

3-Colouring Planar Graphs PartitioningH-minor free graphs into three subgraphs with no large components.J

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:18.565323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ac2fa4c-7e03-4e6f-af97-9b48f8dbde65 · outbound

This paper cites Clustered Coloring of Graphs Excluding a Subgraph and a Minor.

3-Colouring Planar Graphs Clustered Coloring of Graphs Excluding a Subgraph and a Minor

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:20.835991Z

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.

Observation 88e4c879-487b-44a8-8fdb-ed56366e55c4 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 30

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:40:20.666110Z

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.

Observation 8edc4bcb-3545-47d3-9df4-7f27c1096b17 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:23.520068Z

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.

Observation 1998a019-a121-4801-baf6-e3dea8e39735 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:23.337640Z

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.

Observation 0d1b332a-cf32-4cb4-b619-dc19cd0128f7 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:19.166789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 81f4029b-d626-4195-8487-cf71f087fedd · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:23.131775Z

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.

Observation 3116636c-dfc4-44db-a1b3-f61202413d78 · outbound

This paper cites Graphs on surfaces.

3-Colouring Planar Graphs Graphs on surfaces

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:22.874287Z

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.

Observation f6168c38-a207-47d1-aad0-447a25e14f68 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:22.659654Z

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.

Observation 4a8331ac-d9ba-4af7-9e3f-dcd80cb1466e · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:22.468617Z

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.

Observation eff54bc1-32a1-4b65-8a97-74dc9967ff0f · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:19.580304Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bb98771-81a7-4af0-86ab-35ec284216a3 · outbound

This paper cites Sanders, Paul Seymour, and Robin Thomas.

3-Colouring Planar Graphs Sanders, Paul Seymour, and Robin Thomas

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:22.296633Z

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.

Observation 83a10cdb-e0cf-4a21-aff6-e23a1fbe9760 · outbound

This paper cites Graph minors.

3-Colouring Planar Graphs Graph minors

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:22.091462Z

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.

Observation f12005d5-e338-413d-ab66-7fa2a0129a8d · outbound

This paper cites Graph minors.

3-Colouring Planar Graphs Graph minors

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:19.786537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d21d2fde-0e17-444e-bfa1-ab2e90a13e34 · outbound

This paper cites Graph minors.

3-Colouring Planar Graphs Graph minors

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T20:40:19.876055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 15203829-7e77-4cb4-9c5c-ee9541f2c649 · outbound

This paper cites Quickly excluding a planar graph.

3-Colouring Planar Graphs Quickly excluding a planar graph

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:40:21.898225Z

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.

Observation 2bf629d1-9edc-41d2-a724-6ee24b015a3c · outbound

This paper cites Improper Colourings inspired by Hadwiger's Conjecture.

3-Colouring Planar Graphs Improper Colourings inspired by Hadwiger's Conjecture

Reference 44

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:40:20.298242Z

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.

Observation 59fcaef9-ab29-4e49-adb3-4f188aeba743 · outbound

This paper cites an unresolved cited work.

3-Colouring Planar Graphs Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:40:21.749886Z

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.

Pith citing papers

Observation b7c627d0-f6ae-4353-8742-67c2aff5951d · inbound

Optimal tree-decompositions with bags of bounded pathwidth cites this paper.

Optimal tree-decompositions with bags of bounded pathwidth 3-Colouring Planar Graphs

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T05:07:02.479725Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.