Work

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

Year: 2024

Type: article

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.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972724000662

Authors: KAIYANG LAN, FENG LIU, DI WU, YIDONG ZHOU

Institutions: Minnan Normal University, East China Normal University, Nanjing Institute of Technology, Nankai University

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,450

OpenAlex ID: W4402933109

FWCI:

Cites: 30

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Related to: 10