Authors:
J. Czap, S. Jendrol', J. Valiska
Title:
Conflict -free connections of graphs
Source:
Discussiones Mathematicae Graph Theory
Received 04.11.2016, Revised 03.03.2017, Accepted 03.03.2017, doi: 10.7151/dmgt.2036

Abstract:
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.
Keywords:
edge-coloring, conflict-free connection, 2-edge-connected graph, tree\vspace{-4mm}

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