Coloring graphs with no induced five-vertex path or gem

M. Chudnovsky; T. Karthick; P. Maceli; Frederic Maffray

Coloring graphs with no induced five-vertex path or gem

Combinatorics 2021-10-07 v2 Discrete Mathematics

Authors: M. Chudnovsky , T. Karthick , P. Maceli , Frederic Maffray

Abstract

For a graph $G$ , let $\chi(G)$ and $\omega(G)$ respectively denote the chromatic number and clique number of $G$ . We give an explicit structural description of ( $P_5$ ,gem)-free graphs, and show that every such graph $G$ satisfies $\chi(G)\le \lceil\frac{5\omega(G)}{4}\rceil$ . Moreover, this bound is best possible.

Keywords

graph coloring rainbow connection graph theory

Cite

@article{arxiv.1810.06186,
  title  = {Coloring graphs with no induced five-vertex path or gem},
  author = {M. Chudnovsky and T. Karthick and P. Maceli and Frederic Maffray},
  journal= {arXiv preprint arXiv:1810.06186},
  year   = {2021}
}

Comments

This paper is dedicated to the memory of Professor Frederic Maffray

Coloring graphs with no induced five-vertex path or gem

Abstract

Keywords

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