A Note on Coloring $(4K_1, C_4, C_6)$free graphs with a $C_7$
Abstract
Evenholefree graphs are a graph class of much interest. Foley et al. [Graphs Comb. 36(1): 125138 (2020)] have recently studied $(4K_1, C_4, C_6)$free graphs, which form a subclass of evenholefree graphs. Specifically, Foley et al. have shown an algorithm for coloring these graphs via bounded cliquewidth 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.08004
 Bibcode:
 2021arXiv211008004K
 Keywords:

 Mathematics  Combinatorics