Finding a dominating set on bipartite graphs

Authors:
Mathieu Liedloff
Affiliations:
Laboratoire d'Informatique Théorique et Appliquée, Université Paul Verlaine - Metz, 57045 Metz Cedex 01, France
Venue:
Information Processing Letters
Year:
2008

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Abstract

Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O^*(2^n^-^z), where n is the number of vertices of G. As a consequence, our algorithm is able to solve the dominating set problem on bipartite graphs in time O^*(2^n^/^2). Another implication is an algorithm for general graphs whose running time is O(1.7088^n).