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arXiv · 2212.12630

Study of Exoo's Lower Bound for Ramsey number $R(5,5)$

Lachlan Ge·Yasiru Jayasooriya·Alex Qiu·Michael Sun·Victor Yuan
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Abstract

We review Exoo's 1989 paper, which demonstrates that a lower bound for the Ramsey number $R(5,5)$ is $43$. We provide an efficient way to verify the claims in the paper, adding detailed proofs. In particular, we replace the reference to computer verification by concise arguments. Using our understanding of the insight behind these proofs, we are also able to analyse variations of the graph constructions to obtain, for example, colourings of $K_{43}$ which have very few monochromatic $K_5$.

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Lachlan Ge, Yasiru Jayasooriya, Alex Qiu, Michael Sun, Victor Yuan. 2023-03-25. Study of Exoo's Lower Bound for Ramsey number $R(5,5)$. https://arxiv.org/abs/2212.12630

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