Maximum Connected Domatic Partition of Directed Path Graphs with Single Junction

Authors:
Masaya Mito;Satoshi Fujita
Affiliations:
Department of Information Engineering Graduate School of Engineering, Hiroshima University,;Department of Information Engineering Graduate School of Engineering, Hiroshima University,
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

In this paper, we consider the problem of finding a maximum connected domatic partition of a given graph. We propose a polynomial time algorithm for solving the problem for a subclass of directed path graphs which is known as a class of intersection graphs modeled by a set of directed paths on a directed tree. More specifically, we restrict the class of directed path graphs in such a way that the underlying directed tree has at most one node to have several incoming arcs.