Coloring graphs with no induced five-vertex path or gem

Authors

Maria Chudnovsky, Princeton University
T. Karthick, Indian Statistical Institute Chennai
Peter Maceli, Ithaca College
Frédéric Maffray, Sciences pour la Conception, l'Optimisation et la Production de Grenoble (G-SCOP)

Article Type

Research Article

Publication Title

Journal of Graph Theory

Abstract

For a graph (Formula presented.), let (Formula presented.) and (Formula presented.), respectively, denote the chromatic number and clique number of (Formula presented.). We give an explicit structural description of ((Formula presented.), gem)-free graphs, and show that every such graph (Formula presented.) satisfies (Formula presented.). Moreover, this bound is best possible. Here a gem is the graph that consists of an induced four-vertex path plus a vertex which is adjacent to all the vertices of that path.

First Page

527

Last Page

542

DOI

10.1002/jgt.22572

Publication Date

12-1-2020

Comments

Open Access, Green

Recommended Citation

Chudnovsky, Maria; Karthick, T.; Maceli, Peter; and Maffray, Frédéric, "Coloring graphs with no induced five-vertex path or gem" (2020). Journal Articles. 56.
https://digitalcommons.isical.ac.in/journal-articles/56