Paper Citation Record · LEDGER

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs

As of 21 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2607.18569.

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

pith.paper-citation-record.v1
2607.18569 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T15:12:58.254621Z

measured 26 of 26 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 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

26 of 26 outbound references displayed

verified exact6
verified fuzzy0
unresolved16
parse uncertain0
malformed identifier4
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 32167deb-5346-4f63-a8b4-d28415b70796 · outbound

This paper cites More Asymmetry Yields Faster Matrix Multiplication.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs More Asymmetry Yields Faster Matrix Multiplication

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:53.907529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09e28232-06c5-47ee-b92f-416fb307c5f1 · outbound

This paper cites OntheChvátal-ErdösTriangleGame.Electron.J.Comb.,18(1),2011.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs OntheChvátal-ErdösTriangleGame.Electron.J.Comb.,18(1),2011

Reference 2

Resolution: malformed identifier; doi_truncated, observed 2026-08-01T15:13:22.315377Z

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.

Observation bd5345f0-b874-44af-a61c-1c3ec139f885 · outbound

This paper cites O(n2.7799) Complexity for n*n Approximate Matrix Multiplication.Inf.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs O(n2.7799) Complexity for n*n Approximate Matrix Multiplication.Inf

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:54.100692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddaf2be1-bf40-42f1-9f25-b2232fde97fc · outbound

This paper cites Seymour, and Robin Thomas.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Seymour, and Robin Thomas

Reference 4

Resolution: verified exact; doi, observed 2026-08-01T15:13:22.050592Z

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.

Observation 5e576dae-fd2c-49a1-9367-dbb49d8a67f7 · outbound

This paper cites On the Asymptotic Complexity of Matrix multiplication (Extended Summary).

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs On the Asymptotic Complexity of Matrix multiplication (Extended Summary)

Reference 6

Resolution: malformed identifier; no resolver link, observed 2026-08-01T15:12:54.349701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cc3d7ae1-8fba-4963-a9ee-6f537f84dde1 · outbound

This paper cites TowardsOptimalOutput-Sensitive Clique Listing or: Listing Cliques from Smaller Cliques.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs TowardsOptimalOutput-Sensitive Clique Listing or: Listing Cliques from Smaller Cliques

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:54.498766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 752b4553-352a-4f42-9d0e-7a2c38aae272 · outbound

This paper cites Complexity of Maker-Breaker games on edge sets of graphs.Discret.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Complexity of Maker-Breaker games on edge sets of graphs.Discret

Reference 9

Resolution: malformed identifier; no resolver link, observed 2026-08-01T15:12:54.651633Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36c38fcb-3b0e-4e22-83d5-8ab53580de83 · outbound

This paper cites On the complexity of fixed parameter clique and dominating set.Theoretical Computer Science, 326(1):57–67, 2004.doi:10.1016/j.tcs.2004.05.009.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs On the complexity of fixed parameter clique and dominating set.Theoretical Computer Science, 326(1):57–67, 2004.doi:10.1016/j.tcs.2004.05.009

Reference 10

Resolution: verified exact; doi, observed 2026-08-01T15:13:21.929579Z

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.

Observation b1331c2b-6b1a-4141-9f53-5092d7266f09 · outbound

This paper cites Selfridge.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Selfridge

Reference 11

Resolution: malformed identifier; no resolver link, observed 2026-08-01T15:12:55.020314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b54b81e-9360-4311-b3bd-538b267cf71a · outbound

This paper cites 4-uniform Maker-Breaker and Maker-Maker games are PSPACE-complete.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs 4-uniform Maker-Breaker and Maker-Maker games are PSPACE-complete

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:55.237577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86f3387e-424c-476e-9d46-fbf7282c14fe · outbound

This paper cites Maker-Breaker is solved in polynomial time on hypergraphs of rank 3.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Maker-Breaker is solved in polynomial time on hypergraphs of rank 3

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:55.441245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee827ec6-1e1a-47f6-b670-219aef0bb99d · outbound

This paper cites A new bound for the Maker-Breaker triangle game.Eur.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs A new bound for the Maker-Breaker triangle game.Eur

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:55.652037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53840470-6370-4fbb-b0d9-bc4fefedb67d · outbound

This paper cites On the number of triangles in𝑘4-free graphs.CoRR, abs/2509.12100, 2025.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs On the number of triangles in𝑘4-free graphs.CoRR, abs/2509.12100, 2025

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:55.913345Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abb09ad3-5542-4b2d-81d1-1af1cff05365 · outbound

This paper cites Birkhäuser Basel, 2014.doi:10.1007/978-3-0348-0825-5.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Birkhäuser Basel, 2014.doi:10.1007/978-3-0348-0825-5

Reference 16

Resolution: verified exact; doi, observed 2026-08-01T15:13:21.767756Z

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.

Observation 393633f6-189d-4859-a125-94deb2f56ec8 · outbound

This paper cites Hopcroft and Robert Endre Tarjan.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Hopcroft and Robert Endre Tarjan

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:56.342199Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb854d87-d37f-4559-8ef5-2bd3687a79bc · outbound

This paper cites Finding a Minimum Circuit in a Graph.SIAM J.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Finding a Minimum Circuit in a Graph.SIAM J

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:56.582501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da6a2a39-c039-4fcc-b63f-039178809727 · outbound

This paper cites Solving Maker-Breaker Games on 5-uniform hypergraphs is PSPACE-complete.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Solving Maker-Breaker Games on 5-uniform hypergraphs is PSPACE-complete

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:56.751500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4148050-c8fc-47bc-aff0-2c61847e02de · outbound

This paper cites Phd thesis, Freie Universität Berlin, 2004.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Phd thesis, Freie Universität Berlin, 2004

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:56.953724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a1c7c9c-e1df-41ec-9cb1-73032632bbc8 · outbound

This paper cites an unresolved cited work.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:57.166594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dc2eff71-ee90-4c57-a0a6-37f49b6e5084 · outbound

This paper cites AthresholdfortheMaker-Breakercliquegame.RandomStruct.Algorithms,45(2):318–341, 2014.doi:10.1002/RSA.20489.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs AthresholdfortheMaker-Breakercliquegame.RandomStruct.Algorithms,45(2):318–341, 2014.doi:10.1002/RSA.20489

Reference 22

Resolution: verified exact; doi, observed 2026-08-01T15:13:21.648894Z

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.

Observation 83c527ed-abf8-4655-ab54-b5f861a6035e · outbound

This paper cites an unresolved cited work.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Unresolved cited work

Reference 23

Resolution: verified exact; doi, observed 2026-08-01T15:13:21.478689Z

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.

Observation 140a2353-c757-4fe2-8e61-35663ebb95f6 · outbound

This paper cites 6-UniformMaker-BreakerGameisPSPACE-Complete.Combinatorica,43(3):595–612, 2023.doi:10.1007/S00493-023-00026-7.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs 6-UniformMaker-BreakerGameisPSPACE-Complete.Combinatorica,43(3):595–612, 2023.doi:10.1007/S00493-023-00026-7

Reference 24

Resolution: verified exact; doi, observed 2026-08-01T15:13:21.196303Z

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.

Observation 56efdbed-b73c-4205-b8cb-f1bf71e28503 · outbound

This paper cites Some Properties of Disjoint Sums of Tensors Related to Matrix Multiplication.SIAM J.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Some Properties of Disjoint Sums of Tensors Related to Matrix Multiplication.SIAM J

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:57.916569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 084e7b68-1b18-4c9d-b3d0-59a5923e3670 · outbound

This paper cites Schaefer.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Schaefer

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:58.050460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b9ee4aa-f1d3-42ef-a9b7-07f1f90974ac · outbound

This paper cites Partial and Total Matrix Multiplication.SIAM J.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Partial and Total Matrix Multiplication.SIAM J

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:58.185865Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 577d8c96-fcd4-4053-a6ca-277ae346b10e · outbound

This paper cites Multiplying Matrices Faster Than Coppersmith-Winograd.

Faster Algorithms for Deciding the Unbiased Maker-Breaker Triangle Game on General Graphs Multiplying Matrices Faster Than Coppersmith-Winograd

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T15:12:58.254621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.