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THE CHROMATIC NUMBER OF $\boldsymbol {(P_6,C_4,\mbox {diamond})}$-FREE GRAPHS
Part of
- Graph theory
KAIYANG LAN, YIDONG ZHOU, FENG LIU
Journal:

Bulletin of the Australian Mathematical Society / Volume 108 / Issue 1 / August 2023

Published online by Cambridge University Press:

03 October 2022, pp. 1-10

Print publication:

August 2023
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The diamond is the complete graph on four vertices minus one edge; $P_n$ and $C_n$ denote the path and cycle on n vertices, respectively. We prove that the chromatic number of a $(P_6,C_4,\mbox {diamond})$-free graph G is no larger than the maximum of 3 and the clique number of G.