Unique-maximum and conflict-free coloring for hypergraphs and tree graphs

Authors:
Panagiotis Cheilaris;Balázs Keszegh;Dömötör Pálvölgyi
Affiliations:
Center for Advanced Studies in Mathematics, Ben-Gurion University, Be'er Sheva, Israel;Alfréd Rényi Institute of Mathematics, Budapest, Hungary;Eötvös University, Budapest, Hungary
Venue:
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Year:
2012

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Abstract

We investigate the relationship between two kinds of vertex colorings of hypergraphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every hyperedge of the hypergraph the maximum color in the hyperedge occurs in only one vertex of the hyperedge. In a conflict-free coloring, in every hyperedge of the hypergraph there exists a color in the hyperedge that occurs in only one vertex of the hyperedge. We define corresponding unique-maximum and conflict-free chromatic numbers and investigate their relationship in arbitrary hypergraphs. Then, we concentrate on hypergraphs that are induced by simple paths in tree graphs.