Conflict-free chromatic index of bipartite graphs

Abstract

An edge coloring of a graph $G$ is called conflict-free if, for every edge, its closed neighborhood contains a color that appears exactly once. The least number of colors required for such a coloring is the conflict-free chromatic index of $G$, denoted by ${\chi }_{CF}^{\prime }(G)$. Kamyczura, Meszka, and Przybyło conjectured that ${\chi }_{CF}^{\prime }(G)\le 3$ for any bipartite graph $G$ without isolated vertices. In this paper, we confirm this conjecture.

6 pages