Author:
Chudnovsky Maria,Huang Shenwei,Karthick T.,Kaufmann Jenny
Abstract
The claw is the graph $K_{1,3}$, and the fork is the graph obtained from the claw $K_{1,3}$ by subdividing one of its edges once. In this paper, we prove a structure theorem for the class of (claw, $C_4$)-free graphs that are not quasi-line graphs, and a structure theorem for the class of (fork, $C_4$)-free graphs that uses the class of (claw, $C_4$)-free graphs as a basic class. Finally, we show that every (fork, $C_4$)-free graph $G$ satisfies $\chi(G)\leqslant \lceil\frac{3\omega(G)}{2}\rceil$ via these structure theorems with some additional work on coloring basic classes.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
3 articles.
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