Square-free graphs with no six-vertex induced path

Article Type

Research Article

Publication Title

SIAM Journal on Discrete Mathematics

Abstract

We elucidate the structure of (P6, C4)-free graphs by showing that every such graph either has a clique cutset, or a universal vertex, or belongs to several special classes of graphs. Using this result, we show that for any (P6, C4)-free graph G, [Formula presented]\ are tight upper bounds for the chromatic number of G. Moreover, our structural results imply that every (P6,C4)-free 2 graph with no clique cutset has bounded clique-width, and thus the existence of a polynomial-time algorithm that computes the chromatic number (or stability number) of any (P6, C4)-free graph.

First Page

874

Last Page

909

DOI

10.1137/18M1190653

Publication Date

1-1-2019

Comments

Open Access, Green

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