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THE CHROMATIC NUMBER OF $\boldsymbol {(P_6,C_4,\mbox {diamond})}$-FREE GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  03 October 2022

KAIYANG LAN Open the ORCID record for KAIYANG LAN [Opens in a new window] ,
YIDONG ZHOU Open the ORCID record for YIDONG ZHOU [Opens in a new window]  and
FENG LIU Open the ORCID record for FENG LIU [Opens in a new window]
KAIYANG LAN
Affiliation:
Center for Discrete Mathematics, Fuzhou University, Fujian 350003, PR China e-mail: kylan95@126.com
YIDONG ZHOU
Affiliation:
Center for Discrete Mathematics, Fuzhou University, Fujian 350003, PR China e-mail: zoed98@126.com
FENG LIU*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, PR China
*
e-mail: liufeng0609@126.com
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Abstract

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.

Keywords

chromatic numberinduced subgraphℱ-free graph

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 05C17: Perfect graphs 05C69: Dominating sets, independent sets, cliques
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 1 , August 2023 , pp. 1 - 10
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This research was partially supported by a grant from the National Natural Sciences Foundation of China (No. 11971111).

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