Vertex coloring acyclic digraphs and their corresponding hypergraphs

Authors:
Geir Agnarsson;Ágúst S. Egilsson;Magnús M. Halldórsson
Affiliations:
Department of Mathematical Sciences, George Mason University, MS 3F2, 4400 University Drive, Fairfax, VA 22030, USA;Science Institute, University of Iceland, IS-107 Reykjavik, Iceland;Department of Computer Science, University of Iceland, IS-107 Reykjavik, Iceland
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We consider vertex coloring of an acyclic digraph G@? in such a way that two vertices which have a common ancestor in G@? receive distinct colors. Such colorings arise in a natural way when bounding space for various genetic data for efficient analysis. We discuss the corresponding down-chromatic number and derive an upper bound as a function of D(G@?), 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 G@? and D(G@?).