Elsevier

Discrete Applied Mathematics

Volume 231, 20 November 2017, Pages 166-174
Discrete Applied Mathematics

Characterizations of (4K1, C4, C5)-free graphs

https://doi.org/10.1016/j.dam.2016.08.016Get rights and content
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Abstract

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. There has been keen interest in colouring graphs whose forbidden list L contains graphs with four vertices. A recent paper of Lozin and Malyshev (in press) discusses the state of the art on this problem, identifying three outstanding classes: L=(4K1,claw), L=(4K1,claw, co-diamond), and L=(4K1,C4). In this paper we investigate the class of (4K1, C4, C5)-free graphs and show that if G is a (4K1, C4, C5)-free graph, then G either has bounded clique width or is perfect.

Keywords

Graph colouring
(4K1, C4, C5)-free graphs
Perfect graphs

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