• Corpus ID: 239009976

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

  title={A Note on Coloring \$(4K\_1, C\_4, C\_6)\$-free graphs with a \$C\_7\$},
  author={Martin Kouteck'y},
Even-hole-free graphs are a graph class of much interest. Foley et al. [Graphs Comb. 36(1): 125-138 (2020)] have recently studied (4K1, C4, C6)-free graphs, which form a subclass of even-holefree graphs. Specifically, Foley et al. have shown an algorithm for coloring these graphs via bounded clique-width if they contain a C7. In this note, we give a simpler and much faster algorithm via a more restrictive graph parameter, neighborhood diversity. 


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