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

Details Unique-maximum and conflict-free colorings for hypergraphs and tree graphs Unique-maximum and conflict-free colorings for hypergraphs and tree graphs

2010-02-22

arxiv.org/abs/1002.4210v2

Mathematics

Combinatorics

Scientific paper

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 appears only once. In a conflict-free coloring, in every hyperedge of the hypergraph there is a color that appears only once. We concentrate in hypergraphs that are induced by paths in tree graphs.

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