Optimal chromatic bound for (Formula presented.)-free graphs

被引：0
|
作者：
Char A. [1 ]
Karthick T. [1 ]
机构：
[1] Computer Science Unit, Indian Statistical Institute, Chennai Centre, Chennai
来源：
Journal of Graph Theory | 2024年 / 105卷 / 02期
关键词：
chromatic number; clique number; self-complementary graph classes; vertex coloring; χ-boundedness;
D O I：
10.1002/jgt.23009
中图分类号：
学科分类号：
摘要：
For a graph (Formula presented.), let (Formula presented.) ((Formula presented.)) denote its chromatic (clique) number. A (Formula presented.) is the graph obtained by taking the disjoint union of a two-vertex path (Formula presented.) and a three-vertex path (Formula presented.). A (Formula presented.) is the complement graph of a (Formula presented.). In this paper, we study the class of ((Formula presented.))-free graphs and show that every such graph (Formula presented.) with (Formula presented.) satisfies (Formula presented.). Moreover, the bound is tight. Indeed, for any (Formula presented.) and (Formula presented.), there is a ((Formula presented.))-free graph (Formula presented.) with (Formula presented.) and (Formula presented.). © 2023 Wiley Periodicals LLC.
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页码：149 / 178
页数：29
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