On The Domatic Number of Bipartite Permutation Graphs

Abstract

This paper studies the problem of partitioning the vertices of a graph G into disjoint set V1, …, Vq such that V1, …, Va are all dominating sets of G. The objective is to find the largest q. We first propose a 0-1 matrix representation of bipartite permutation graphs. Then, a linear-time algorithm for domatic number problem on bipartite permutation graphs is designed.