Maximum connected domatic partition of directed path graphs with single junction

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. © 2008 Springer-Verlag Berlin Heidelberg.