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A NOTE ON $\chi $-BINDING FUNCTIONS AND LINEAR FORESTS

Part of: Graph theory

Published online by Cambridge University Press:  27 September 2024

KAIYANG LAN Open the ORCID record for KAIYANG LAN [Opens in a new window] ,
FENG LIU Open the ORCID record for FENG LIU [Opens in a new window] ,
DI WU Open the ORCID record for DI WU [Opens in a new window]  and
YIDONG ZHOU Open the ORCID record for YIDONG ZHOU [Opens in a new window]
KAIYANG LAN
Affiliation:
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou Fujian, 363000, PR China e-mail: kylan95@126.com
FENG LIU*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, PR China
DI WU
Affiliation:
Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, Jiangsu, PR China e-mail: 1975335772@qq.com
YIDONG ZHOU
Affiliation:
College of Computer Science, Nankai University, Tianjin 300350, PR China e-mail: zoed98@126.com
*
e-mail: liufeng0609@126.com
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Abstract

Let G and H be two vertex disjoint graphs. The join $G+H$ is the graph with $V(G+H)=V(G)+V(H)$ and $E(G+H)=E(G)\cup E(H)\cup \{xy\;|\; x\in V(G), y\in V(H)\}$. A (finite) linear forest is a graph consisting of (finite) vertex disjoint paths. We prove that for any finite linear forest F and any nonnull graph H, if $\{F, H\}$-free graphs have a $\chi $-binding function $f(\omega )$, then $\{F, K_n+H\}$-free graphs have a $\chi $-binding function $kf(\omega )$ for some constant k.

Keywords

chromatic numberPt-freeinduced subgraph

MSC classification

Primary: 05C15: Coloring of graphs and hypergraphs
Secondary: 05C17: Perfect graphs 05C69: Dominating sets, independent sets, cliques

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 112 , Issue 1 , August 2025 , pp. 23 - 29
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This paper was partially supported by grants from the National Natural Sciences Foundation of China (No. 12271170) and Science and Technology Commission of Shanghai Municipality (STCSM) (No. 22DZ2229014).

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