Abstract
We consider vertex coloring of a simple acyclic digraph \(\overline{G}\) in such a way that two vertices which have a common ancestor in \(\overline{G}\) 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.
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Agnarsson, G., Egilsson, Á.S., Halldórsson, M.M. (2004). Proper Down-Coloring Simple Acyclic Digraphs. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds) Applications of Graph Transformations with Industrial Relevance. AGTIVE 2003. Lecture Notes in Computer Science, vol 3062. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25959-6_22
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DOI: https://doi.org/10.1007/978-3-540-25959-6_22
Publisher Name: Springer, Berlin, Heidelberg
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