Note: On the inapproximability of independent domination in 2P3-free perfect graphs

Authors:
Yury L. Orlovich;Valery S. Gordon;Dominique de Werra
Affiliations:
Faculty of Applied Mathematics and Computer Science, Belarus State University, Nezavisimosti Av. 4, 220030 Minsk, Belarus;United Institute of Informatics Problems, National Academy of Sciences of Belarus, 6 Surganova Street, 220012 Minsk, Belarus;Ecole Polytechnique Fédérale de Lausanne (EPFL), Recherche Opérationnelle Sud-Est (ROSE), CH-1015 Lausanne, Switzerland
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We consider the complexity of approximation for the IndependentDominating Set problem in 2P3-free graphs, i.e., graphs thatdo not contain two disjoint copies of the chordless path on threevertices as an induced subgraph. We show that, if P≠NP, theproblem cannot be approximated for 2P3-free graphs inpolynomial time within a factor of n1-εfor any constant ε0, where n is the number of verticesin the graph. Moreover, we show that the result holds even if the2P3-free graph is restricted to being weakly chordal (andthereby perfect).