On the Chromatic Number of (P6 , Diamond)-Free Graphs

Article Type

Research Article

Publication Title

Graphs and Combinatorics

Abstract

In this paper, we first show that every (P6, diamond, K4)-free graph is 6-colorable. We also give an example of a (P6, diamond, K4)-free graph G with χ(G) = 6. Further, we show that for every (P6, diamond)-free graph G, the chromatic number of G is upper bounded by a linear function of its clique number. This generalizes some known results in the literature.

First Page

677

Last Page

692

DOI

10.1007/s00373-018-1905-9

Publication Date

7-1-2018

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