### References & Citations

# Mathematics > Combinatorics

# Title: A Note on Coloring $(4K_1, C_4, C_6)$-free graphs with a $C_7$

(Submitted on 15 Oct 2021)

Abstract: Even-hole-free graphs are a graph class of much interest. Foley et al. [Graphs Comb. 36(1): 125-138 (2020)] have recently studied $(4K_1, C_4, C_6)$-free graphs, which form a subclass of even-hole-free graphs. Specifically, Foley et al. have shown an algorithm for coloring these graphs via bounded clique-width if they contain a $C_7$. In this note, we give a simpler and much faster algorithm via a more restrictive graph parameter, neighborhood diversity.

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