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Paper Citation Record · LEDGER

Online Edge Coloring: Sharp Thresholds

As of 21 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2507.21560.

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

pith.paper-citation-record.v1
2507.21560 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:49:06.676513Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-17T21:26:29.185866Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-17T21:30:18.446471Z

Reference resolution

18 of 18 outbound references displayed

  • verified exact0
  • verified fuzzy17
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9ae81be9-5ed8-4ec2-be07-f9803d368eb7 · outbound

This paper cites Vizing's theorem in near-linear time.

Online Edge Coloring: Sharp Thresholds Vizing's theorem in near-linear time

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:11.622645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.140827Z digest=sha256:6f115699eb5d19d6cfe517237c895a15c3a94d286b1ec00f2a2c974c2f21a017

Observation 707dc13e-afdd-4376-8af8-bb428235adfe · outbound

This paper cites Switch scheduling via randomized edge coloring.

Online Edge Coloring: Sharp Thresholds Switch scheduling via randomized edge coloring

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:11.371111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.294590Z digest=sha256:a3210639eb5f27dab5067a6088d942b86e059703eb5b68f85e75f8b72d4d3e0d

Observation 6bea523a-a754-407a-8a41-5dadf405fcaa · outbound

This paper cites On the power of randomization in on-line algorithms.

Online Edge Coloring: Sharp Thresholds On the power of randomization in on-line algorithms

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:11.069811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.463686Z digest=sha256:7860523ac81236f78b0eba9b51e5aaf0197edaec36b7e7e2d7f7005874cf07ba

Observation 70d20273-3e45-4466-a8fb-074f0182feda · outbound

This paper cites Online edge coloring algorithms via the nibble method.

Online Edge Coloring: Sharp Thresholds Online edge coloring algorithms via the nibble method

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:10.760390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.590592Z digest=sha256:c1f1be5d0813869e99bfe232a2ec545bba5281e83e6312ab7e08ad70ee0b9d01

Observation ee49517a-006e-4c6d-b178-22284ba8d3a6 · outbound

This paper cites Online graph edge-coloring in the random-order arrival model.

Online Edge Coloring: Sharp Thresholds Online graph edge-coloring in the random-order arrival model

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:10.482636Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.807206Z digest=sha256:5f1894f02c86632570890785fcfdb0fe7a5d908a5c0d47b9dda835b9625bb855

Observation fe468f96-2d42-4176-ac62-59521f233521 · outbound

This paper cites The greedy algorithm is optimal for on-line edge coloring.

Online Edge Coloring: Sharp Thresholds The greedy algorithm is optimal for on-line edge coloring

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:10.161384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:04.987619Z digest=sha256:c019abf039d2a8849245c81d6bc49132461f299292e6317c49135826d82ae760

Observation 88367e03-1d19-44c6-9d84-6863ed1188b2 · outbound

This paper cites Online edge coloring is (nearly) as easy as offline.

Online Edge Coloring: Sharp Thresholds Online edge coloring is (nearly) as easy as offline

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:09.847026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.130578Z digest=sha256:903c17213f4665a36a68a43e0ecee2b3aff240ddc3b8863e87edd77a1128cc5b

Observation dba607ed-cc26-4e3d-9c0c-0c74143bd32a · outbound

This paper cites Simple and optimal online bipartite edge coloring.

Online Edge Coloring: Sharp Thresholds Simple and optimal online bipartite edge coloring

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:09.466581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.287188Z digest=sha256:73d137cf585bd33e80b61d528ccf9c7bd1706a8f093a491a5ee6c5ee72be3a59

Observation 4bbb54da-6fd1-4f58-bd30-e3376a7a3556 · outbound

This paper cites Deterministic online bipartite edge coloring.

Online Edge Coloring: Sharp Thresholds Deterministic online bipartite edge coloring

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:09.167846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.419472Z digest=sha256:a376bd6ea080aaf9dd382d3fbd1e7b6c4e9ea186c25940f038a3577116cb0fa3

Observation 357b00d3-eb60-4370-a848-ff0c8d59de24 · outbound

This paper cites Tight bounds for online edge coloring.

Online Edge Coloring: Sharp Thresholds Tight bounds for online edge coloring

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:08.914663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.593213Z digest=sha256:bcc0a2a77556d77b32688f205579d23335b1908d8f6194ce044c624fe3f3d532

Observation b0b11143-86fc-41c4-a8cf-4b5e5421c604 · outbound

This paper cites Randomized greedy online edge coloring succeeds for dense and randomly-ordered graphs.

Online Edge Coloring: Sharp Thresholds Randomized greedy online edge coloring succeeds for dense and randomly-ordered graphs

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:08.639997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.739319Z digest=sha256:644f0c3d82f3161c359d6657805f3123f84d8da19fc8b404b23d0f4876c2b0d5

Observation 671e0d1d-061a-4598-8c05-2e7ad442ef05 · outbound

This paper cites The np-completeness of edge-coloring.

Online Edge Coloring: Sharp Thresholds The np-completeness of edge-coloring

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:08.344883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:05.880797Z digest=sha256:79e9a71f9f626b4f8c8ad572139c1d84a3c8b99f0d779adeca5418bd2df51927

Observation 806d39c4-4a64-44a1-83ce-13aa8a4c4d0e · outbound

This paper cites Asymptotically good list-colorings.

Online Edge Coloring: Sharp Thresholds Asymptotically good list-colorings

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:08.081062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:06.006583Z digest=sha256:409e8275afe0705cc48372417d3108aa46d5698ab5842e3e812fcf0066b56612

Observation dd029ebf-6bfb-4d75-9dbb-97aa6624d87f · outbound

This paper cites Online edge coloring via tree recurrences and correlation decay.

Online Edge Coloring: Sharp Thresholds Online edge coloring via tree recurrences and correlation decay

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:07.836862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:06.142322Z digest=sha256:901f24fc89ca2e4fb18d91e3068bed596685c11fc0c3e89e17007f542caa717f

Observation 6f3a67d9-18de-4e1b-913a-5074356dadd3 · outbound

This paper cites Solutions of ordinary differential equations as limits of pure jump markov processes.

Online Edge Coloring: Sharp Thresholds Solutions of ordinary differential equations as limits of pure jump markov processes

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:07.554820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:06.292169Z digest=sha256:d0331ba821f815938e98861f3c0102af530efae94ad343b0d869bf3573b9ce2e

Observation 77604b77-a18c-4473-bed5-d29ecf1d09e8 · outbound

This paper cites The greedy algorithm is not optimal for on-line edge coloring.

Online Edge Coloring: Sharp Thresholds The greedy algorithm is not optimal for on-line edge coloring

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:07.281682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:06.411422Z digest=sha256:cf12615a938f2fa0ccab57f6ae9e214eab7018545e57ae83b6a680d60c6388ff

Observation c1f84754-0d6f-4c52-b597-9af78c2477ab · outbound

This paper cites On an estimate of the chromatic class of a p-graph.

Online Edge Coloring: Sharp Thresholds On an estimate of the chromatic class of a p-graph

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-06T12:49:06.545255Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T12:49:06.545255Z digest=sha256:21a14223b5db79f44eb3894bd64726781c41393e0e54592d39ba1cdc96691e7e

Observation f678da36-d9db-4c3e-b991-4c0594089ac4 · outbound

This paper cites Probabilistic computations: Toward a unified measure of complexity.

Online Edge Coloring: Sharp Thresholds Probabilistic computations: Toward a unified measure of complexity

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T12:49:06.953252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=arxiv_source observed=2026-08-06T12:49:06.676513Z digest=sha256:1e14712447b517dea85ae602a0ffcaa4d286358fd6da0346be79376781b279f0

Pith citing papers

Observation 83ed5364-f906-4ea0-85f4-421f5a570338 · inbound

Online Graph Coloring for $k$-Colorable Graphs cites this paper.

Online Graph Coloring for $k$-Colorable Graphs Online Edge Coloring: Sharp Thresholds

Reference 8

Resolution
verified exact
arxiv_id, observed 2026-05-17T21:30:18.448175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-05-17T21:26:29.185866Z digest=sha256:dd3cef2a63ccddd78756af0af01a8ba93c326dd000dc6e09cc98edef1514cd24