Colouring Squares of Claw-free Graphs
Colouring Squares of Claw-free Graphs
Abstract Is there some absolute $\unicode[STIX]{x1D700}>0$ such that for any claw-free graph $G$ , the chromatic number of the square of $G$ satisfies $\unicode[STIX]{x1D712}(G^{2})\leqslant (2-\unicode[STIX]{x1D700})\unicode[STIX]{x1D714}(G)^{2}$ , where $\unicode[STIX]{x1D714}(G)$ is the clique number of $G$ ? Erdős and Nešetřil asked this question for the specific case where $G$ is the line …