Vertex coloring acyclic digraphs and their corresponding hypergraphs

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).

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Geir Agnarsson, Ágúst S. Egilsson, Magnús M. Halldórsson
• Keywords: Corresponding Down-chromatic Number, DAM 2008, Down-chromatic Number, Upper Bound