A BOUND FOR THE CHROMATIC NUMBER OF (, GEM)-FREE GRAPHS

Author:

CAMERON KATHIEORCID,HUANG SHENWEIORCID,MERKEL OWENORCID

Abstract

As usual, $P_{n}$ ($n\geq 1$) denotes the path on $n$ vertices. The gem is the graph consisting of a $P_{4}$ together with an additional vertex adjacent to each vertex of the $P_{4}$. A graph is called ($P_{5}$, gem)-free if it has no induced subgraph isomorphic to a $P_{5}$ or to a gem. For a graph $G$, $\unicode[STIX]{x1D712}(G)$ denotes its chromatic number and $\unicode[STIX]{x1D714}(G)$ denotes the maximum size of a clique in $G$. We show that $\unicode[STIX]{x1D712}(G)\leq \lfloor \frac{3}{2}\unicode[STIX]{x1D714}(G)\rfloor$ for every ($P_{5}$, gem)-free graph $G$.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 8 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Divisibility and coloring of some P5-free graphs;Discrete Applied Mathematics;2024-05

2. Some results on k-critical P5-free graphs;Discrete Applied Mathematics;2023-07

3. A Tight Linear Bound to the Chromatic Number of $$(P_5, K_1+(K_1\cup K_3))$$-Free Graphs;Graphs and Combinatorics;2023-04-04

4. Colouring graphs with no induced six-vertex path or diamond;Theoretical Computer Science;2023-01

5. On the chromatic number of some P5-free graphs;Discrete Mathematics;2022-10

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