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arXiv · 1904.08180

The intersection of two vertex coloring problems

Angele M. Foley·Dallas J. Fraser·Chinh T. Hoang·Kevin Holmes·Tom P. LaMantia
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Abstract

A hole is an induced cycle with at least four vertices. A hole is even if its number of vertices is even. Given a set L of graphs, a graph G is L-free if G does not contain any graph in L as an induced subgraph. Currently, the following two problems are unresolved: the complexity of coloring even hole-free graphs, and the complexity of coloring {4K1, C4}-free graphs. The intersection of these two problems is the problem of coloring {4K1, C4, C6}-free graphs. In this paper we present partial results on this problem.

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Angele M. Foley, Dallas J. Fraser, Chinh T. Hoang, Kevin Holmes, Tom P. LaMantia. 2019-04-17. The intersection of two vertex coloring problems. https://arxiv.org/abs/1904.08180

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