Solving Graph Coloring Problems with Abstraction and Symmetry

Michael Codish, Michael Frank, Avraham Itzhakov, Alice Miller

Research output: Working paper/PreprintPreprint

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This paper introduces a general methodology, based on abstraction and symmetry, that applies to solve hard graph edge-coloring problems and demon strates its use to provide further evidence that the Ramsey number R(4, 3, 3) = 30. 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 more than 50 years. We illustrate our approach by showing that: (1) there are precisely
78,892 (3,3, 3; 13) Ramsey colorings; and (2) if there existsa (4,3, 3; 30) Ramsey coloring then it is (13,8,8) regular. Specifically each node has 13 edges in the first color, 8 in the second, and 8 in the third. We conjecture that these two results will help provide a proof that no o (4, 3, 3; 30) Ramsey
coloring exists implying that R(4 3, 3) = 30.
Original languageEnglish GB
StatePublished - 18 Sep 2014

Publication series

NamearXiv:1612.08154 [cs]


  • cs.AI
  • cs.DM


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