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arXiv · 1510.08266

Computing the Ramsey Number R(4,3,3) using Abstraction and Symmetry breaking

Michael Codish·Michael Frank·Avraham Itzhakov·Alice Miller
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Abstract

The number $R(4,3,3)$ is often presented as the unknown Ramsey number with the best chances of being found "soon". Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on \emph{abstraction} and \emph{symmetry breaking} that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value $R(4,3,3)=30$. Along the way it is required to first compute the previously unknown set ${\cal R}(3,3,3;13)$ consisting of 78{,}892 Ramsey colorings.

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Michael Codish, Michael Frank, Avraham Itzhakov, Alice Miller. 2015-11-01. Computing the Ramsey Number R(4,3,3) using Abstraction and Symmetry breaking. https://arxiv.org/abs/1510.08266

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