Graph unique-maximum and conflict-free colorings

Authors:
Panagiotis Cheilaris;Géza Tóth
Affiliations:
Center for Advanced Studies in Mathematics, Ben-Gurion University, P.O.B. 653, Beer Sheva 84105, Israel;Alfréd Rényi Institute, Hungarian Academy of Sciences, 13-15 Reáltonoda utca, Budapest 1053, Hungary
Venue:
Journal of Discrete Algorithms
Year:
2011

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Abstract

We investigate the relationship between two kinds of vertex colorings of graphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color appears only once. In a conflict-free coloring, in every path of the graph there is a color that appears only once. We also study computational complexity aspects of conflict-free colorings and prove a completeness result. Finally, we improve lower bounds for those chromatic numbers of the grid graph.