Unique-maximum and conflict-free colorings for hypergraphs and tree graphs
Combinatorics
2012-06-12 v3
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 appears only once. In a conflict-free coloring, in every hyperedge of the hypergraph there is a color that appears only once. 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.
Cite
@article{arxiv.1002.4210,
title = {Unique-maximum and conflict-free colorings for hypergraphs and tree graphs},
author = {Panagiotis Cheilaris and Balázs Keszegh and Dömötör Pálvölgyi},
journal= {arXiv preprint arXiv:1002.4210},
year = {2012}
}
Comments
added some references and expanded some proofs