Proper down-coloringSimple acyclic digraphs

Abstract

We considervertex coloring of a simple 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 clustering, indexing and bounding space for various genetic data for efficient analysis. We discuss the corresponding chromatic number and derive an upper bound as a function of the maximum number of descendants of a given vertex and the inductiveness of the corresponding hypergraph, which is obtained from the original digraph. ©Springer-Verlag 2004.