On independence domination

Authors:
Wing-Kai Hon;Ton Kloks;Hsiang-Hsuan Liu;Sheung-Hung Poon;Yue-Li Wang
Affiliations:
National Tsing Hua University, Taiwan;National Tsing Hua University, Taiwan;National Tsing Hua University, Taiwan;National Tsing Hua University, Taiwan;National Taiwan University of Science and Technology, Taiwan
Venue:
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
Year:
2013

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Abstract

Let G be a graph. The independence-domination number γi(G) is the maximum over all independent sets I in G of the minimal number of vertices needed to dominate I. In this paper we investigate the computational complexity of γi(G) for graphs in several graph classes related to cographs. We present an exact exponential algorithm. We show that there is a polynomial-time algorithm to compute a maximum independent set in the Cartesian product of two cographs. We prove that independence domination is NP-hard for planar graphs and we present a PTAS.