Square-free graphs with no induced fork

Article Type

Research Article

Publication Title

Electronic Journal of Combinatorics

Abstract

The claw is the graph K1,3, and the fork is the graph obtained from the claw K1,3 by subdividing one of its edges once. In this paper, we prove a structure theorem for the class of (claw, C4)-free graphs that are not quasi-line graphs, and a structure theorem for the class of (fork, C4)-free graphs that uses the class of (claw, C4)-free graphs as a basic class. Finally, we show that every (fork, C4)-free graph G satisfies (formula presented) via these structure theorems with some additional work on coloring basic classes.

DOI

10.37236/9144

Publication Date

1-1-2021

Comments

Open Access, Gold

This document is currently not available here.

Share

COinS