On the clique number of the square of a line graph and its relation to maximum degree of the line graph
Maxime Faron, Luke Postle · Journal of Graph Theory · 2019
Abstract In 1985, Erdős and Nešetřil conjectured that the square of the line graph of a graph , that is, , can be colored with colors. This conjecture implies the weaker conjecture that the clique number of such a graph, that is, , is at most . In 2015, Śleszyńska‐Nowak proved that . In this paper, we prove that . This theorem follows from our stronger result that where .