Abstract
A hole is a chordless 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 $$(4K_1, C_4)$$-free graphs. The intersection of these two problems is the problem of coloring $$(4K_1, C_4, C_6)$$-free graphs. In this paper we present partial results on this problem.
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