Conflict-free connections of graphs
Július Czap, Stanislav Jendrol′, Juraj Valiska · Discussiones Mathematicae Graph Theory · 2018
An edge-colored graph G is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. In this paper the question for the smallest number of colors needed for a coloring of edges of G in order to make it conflict-free connected is investigated. We show that the answer is easy for 2-edge-connected graphs and very difficult for other connected graphs, including trees.