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$R(5,5)\le 46$

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arxiv 2409.15709 v2 pith:WJ4GYOT5 submitted 2024-09-24 math.CO

Vigleik Angeltveit , Brendan D. McKay This is my paper · ORCID
classification math.CO
keywords numberauthorscasescheckingcombinationcomputationscomputerconsistent
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abstract

We prove that the Ramsey number $R(5,5)$ is less than or equal to~$46$. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computations were independently implemented by both authors, with consistent results.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Computer-assisted graph theory: a survey

    math.CO 2025-08 accept novelty 4.0 of 10

    Computer-assisted graph theory is surveyed, and two small computational results are added: i(5) <= 8/28 and non-planarity of the sequence 73517.

  2. Random-projector quantum diagnostics of Ramsey numbers and a prime-factor heuristic for $R(5,5)=45$

    quant-ph 2025-08 reject novelty 4.0 of 10

    The paper claims its random-projector diagnostics identify R(5,5)=45 and estimate R(6,6)=115 and R(7,7)=209, but the critical comparison at n=45 uses different settings than the other sizes.

  3. Upper bounds on diagonal Ramsey numbers [after Campos, Griffiths, Morris, and Sahasrabudhe]

    math.CO 2024-11 accept novelty 2.0 of 10

    An expository Bourbaki survey presenting the 2023 proof that r(k) ≤ (4−δ)^k via the CGMS book algorithm and the Balister et al. geometric refinement lemma, with explicit marking of every non-rigorous step.

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