On proper colorings of hypergraphs

Details On proper colorings of hypergraphs On proper colorings of hypergraphs

2011-11-07

arxiv.org/abs/1111.1558v1

Mathematics

Combinatorics

10 pages, 3 figure

Scientific paper

Let $\mathcal{H}$ be a hypergraph of maximal vertex degree $\Delta$, such that each its hyperedge contains at least $\delta$ vertices. Let $k=\lceil\frac{2\Delta}{\delta}\rceil$. We prove that (i) The hypergraph $\mathcal{H}$ admits proper vertex coloring in $k+1$ colors. (ii) The hypergraph $\mathcal{H}$ admits proper vertex coloring in $k$ colors, if $\delta\ge 3$ and $k\ge 3$. As a consequence of these results we derive upper bounds on the number of colors in dynamic colorings.

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