Enhancing the Erdős‐Lovász Tihany Conjecture for line graphs of multigraphs
Yue Wang, Gexin Yu · Journal of Graph Theory · 2022
Abstract In this paper, we prove an enhanced version of the Erdős‐Lovász Tihany Conjecture for line graphs of multigraphs. That is, for every line graph whose chromatic number is more than its clique number and for any nonnegative integer , any two integers with , there is a partition of the vertex set such that and . In particular, when , we can obtain the same result just for any . The Erdős‐Lovász Tihany conjecture for line graphs is a special case when .