Conflict-Free Coloring: Graphs of Bounded Clique-Width and Intersection Graphs

Sriram Bhyravarapu, Tim A. Hartmann, Hung P. Hoang, Subrahmanyam Kalyanasundaram, I. Vinod Reddy

Abstract: A conflict-free coloring of a graph G is a (partial) coloring of its vertices such that every vertex u has a neighbor whose assigned color is unique in the neighborhood of u. There are two variants of this coloring, one defined using the open neighborhood and one using the closed neighborhood. For both variants, we study the problem of deciding whether the conflict-free coloring of a given graph G is at most a given number k.