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arXiv · 0706.1539

Vertex coloring acyclic digraphs and their corresponding hypergraphs

Geir Agnarsson·Agust Egilsson·Magnus Mar Halldorsson
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Abstract

We consider vertex coloring of an acyclic digraph $\Gdag$ in such a way that two vertices which have a common ancestor in $\Gdag$ receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding {\em down-chromatic number} and derive an upper bound as a function of $D(\Gdag)$, the maximum number of descendants of a given vertex, and the degeneracy of the corresponding hypergraph. Finally we determine an asymptotically tight upper bound of the down-chromatic number in terms of the number of vertices of $\Gdag$ and $D(\Gdag)$.

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Geir Agnarsson, Agust Egilsson, Magnus Mar Halldorsson. 2007-06-11. Vertex coloring acyclic digraphs and their corresponding hypergraphs. https://arxiv.org/abs/0706.1539

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