Paper Citation Record · LEDGER

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

As of 11 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2507.10037.

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

pith.paper-citation-record.v1
2507.10037 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:58:51.118870Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:43:41.152904Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:43:41.256924Z

Reference resolution

31 of 31 outbound references displayed

verified exact5
verified fuzzy19
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c4ccafe5-cfc0-4dc8-bc22-24b6ec31636e · outbound

This paper cites Beyond the classification theorem of Cameron, Goethals, Seidel, and Shult, arXiv:2404.13136, 2024.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Beyond the classification theorem of Cameron, Goethals, Seidel, and Shult, arXiv:2404.13136, 2024

Reference 1

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:58:52.687027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 01b0b035-7203-4dcf-a6e7-78bcbee1b749 · outbound

This paper cites Maximum cuts and judicious partitions in graphs without short cycles.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Maximum cuts and judicious partitions in graphs without short cycles

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:59.110776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c495c78a-316e-46e1-9d07-16f4fcb58b03 · outbound

This paper cites Quasi-randomness and algorithmic regularity for graphs with general degree distributions.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Quasi-randomness and algorithmic regularity for graphs with general degree distributions

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:58.863873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 30558933-14f6-41fc-a0a4-f2b016dfa7e2 · outbound

This paper cites Efficient testing of large graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Efficient testing of large graphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:58.669918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cd0d74b4-c76a-4e4f-a54a-4cad699566f8 · outbound

This paper cites Quadratic forms on graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Quadratic forms on graphs

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:58.541120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 420e5ae1-98f5-4c58-95b8-1bc144ec46cb · outbound

This paper cites Equiangular lines via matrix projection, arXiv:2110.15842, 2024.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Equiangular lines via matrix projection, arXiv:2110.15842, 2024

Reference 6

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:58:52.298076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 09cfc524-bb5f-40a8-81b3-0339ac1a4028 · outbound

This paper cites Factorization norms and an inverse theorem for MaxCut.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Factorization norms and an inverse theorem for MaxCut

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:47.974353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d5cc046-1dd7-44fb-bb52-f4e80b4fc399 · outbound

This paper cites On MaxCut and the Lov´ asz theta function.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut On MaxCut and the Lov´ asz theta function

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:58.233044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 13264379-0d2f-4068-99af-95e773de4f47 · outbound

This paper cites Note on the second eigenvalue of regular graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Note on the second eigenvalue of regular graphs

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:58:51.944595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d3fe1e54-a854-4f97-b338-c276244e76fa · outbound

This paper cites an unresolved cited work.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:57.927393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 521652c8-25cb-4248-b16f-0070d7e40b8c · outbound

This paper cites Lower bounds for max-cut in H-free graphs via semidefinite programming.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Lower bounds for max-cut in H-free graphs via semidefinite programming

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:57.684951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cf947e01-9be7-432f-8e7a-2651dfcb0738 · outbound

This paper cites Maximizing quadratic programs: extending Grothendieck’s inequality.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Maximizing quadratic programs: extending Grothendieck’s inequality

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:57.445737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 158014c9-f920-4eba-ad58-1c2e1564d563 · outbound

This paper cites Quasirandom Cayley graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Quasirandom Cayley graphs

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:57.060060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation dff7267a-53dc-49ce-a2eb-657a34125c45 · outbound

This paper cites Graphs with least eigenvalue−2: ten years on.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Graphs with least eigenvalue−2: ten years on

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:56.766309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b842a452-7b9a-45ff-aaef-2c6f4044e364 · outbound

This paper cites an unresolved cited work.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:56.477779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3a22ce8c-b2c8-485f-ba2e-33f3f6ba99dc · outbound

This paper cites an unresolved cited work.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:56.173077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d52c4486-81fb-4743-97ef-e19e5c9cc53d · outbound

This paper cites an unresolved cited work.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:55.877667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a144fa81-0c0b-4d9d-9cbe-b3710b9452d8 · outbound

This paper cites New results for MaxCut in H-free graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut New results for MaxCut in H-free graphs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:55.616353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0a605507-8551-4adf-bd05-e493f3fd5081 · outbound

This paper cites The energy of a graph: Old and new results.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut The energy of a graph: Old and new results

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:55.345704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6987bbd0-1165-4a3d-a057-d1037d5a32a6 · outbound

This paper cites Approximately strongly regular graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Approximately strongly regular graphs

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:55.049322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 464a0bea-b54d-4fe4-a5f5-aade1f3d48d2 · outbound

This paper cites Beyond the maxcut problem in H-free graphs.Personal Communication.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Beyond the maxcut problem in H-free graphs.Personal Communication

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:54.791860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 41cac458-e7ca-4ae6-8f53-1836ce0c4d16 · outbound

This paper cites Koolen, and Jae Young Yang.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Koolen, and Jae Young Yang

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:54.498827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ccdbf03e-18ee-4b64-a825-f2f2b9825aa2 · outbound

This paper cites An improved bound for strongly regular graphs with smallest eigenvalue −m, arXiv:2506.04964, 2025.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut An improved bound for strongly regular graphs with smallest eigenvalue −m, arXiv:2506.04964, 2025

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:58:51.682780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c87db0a6-5553-4847-a786-0bad267b83fc · outbound

This paper cites Koolen, Meng-Yue Cao, and Qianqian Yang.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Koolen, Meng-Yue Cao, and Qianqian Yang

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:54.212498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 89a53ddd-be89-4f68-a460-1247a8e6713c · outbound

This paper cites Neumaier.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Neumaier

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:53.975867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 93e0de27-0e38-483a-9726-c3581e59c56b · outbound

This paper cites Induced subgraph density. VI. Bounded VC-dimension.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Induced subgraph density. VI. Bounded VC-dimension

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T17:58:50.577237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 77c2933d-2e56-46dc-9c91-9a1232143d32 · outbound

This paper cites an unresolved cited work.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:58:53.718002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 654a209f-6229-4cb3-a946-7aa02264ace7 · outbound

This paper cites Large cuts in hypergraphs via energy.Mathematical Proceedings of the Cambridge Philosophical Society, page 1–17, May 2025.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Large cuts in hypergraphs via energy.Mathematical Proceedings of the Cambridge Philosophical Society, page 1–17, May 2025

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:53.481722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e4780177-24f3-48b2-925b-18aeea99be0a · outbound

This paper cites Positive discrepancy, MaxCut, and eigenvalues of graphs.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Positive discrepancy, MaxCut, and eigenvalues of graphs

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:58:51.396816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation af008d93-d53c-44ac-ab57-faa182942fc4 · outbound

This paper cites Matrix discrepancy and the log-rank conjecture.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Matrix discrepancy and the log-rank conjecture

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:53.249724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 643dfa86-fa8f-47ec-8f6e-f943b2477119 · outbound

This paper cites Graph partitioning: an updated survey.

An Alon-Boppana--type bound for very dense graphs, with applications to max-cut Graph partitioning: an updated survey

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:58:52.963231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation f3690f6b-3d14-42c6-b4cb-4c3df3bf473a · inbound

Beyond the MaxCut problem in $H$-free graphs cites this paper.

Beyond the MaxCut problem in $H$-free graphs An Alon-Boppana--type bound for very dense graphs, with applications to max-cut

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:43:41.317462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.