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Independent Sets in Classes Related to Chair-Free Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9602))

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Abstract

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. MWIS is known to be NP-complete in general, but solvable in polynomial time in classes of \(S_{i,j,k}\)-free graphs, where \(S_{i,j,k}\) is the graph consisting of three induced paths of lengths i, j, k with a common initial vertex. The complexity of the MWIS problem for \(S_{1, 2, 2}\)-free graphs, and for \(S_{1, 1, 3}\)-free graphs are open. In this paper, we show that the MWIS problem can solved in polynomial time for (\(S_{1, 2, 2}\), \(S_{1, 1, 3}\), co-chair)-free graphs, by analyzing the structure of the subclasses of this class of graphs. This extends some known results in the literature.

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Acknowledgements

The author sincerely thanks Prof. Vadim. V. Lözin and Prof. Frédéric Maffray for the fruitful discussions, for their valuable suggestions, and for the feedback provided by them.

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Authors and Affiliations

  1. Computer Science Unit, Indian Statistical Institute, Chennai Centre, Chennai, 600 113, India

    T. Karthick

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  1. T. Karthick
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Correspondence to T. Karthick .

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Editors and Affiliations

  1. Indian Institute of Science, Bangalore, India

    Sathish Govindarajan

  2. Carleton University, Ottawa, ON, Canada

    Anil Maheshwari

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Karthick, T. (2016). Independent Sets in Classes Related to Chair-Free Graphs. In: Govindarajan, S., Maheshwari, A. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2016. Lecture Notes in Computer Science(), vol 9602. Springer, Cham. https://doi.org/10.1007/978-3-319-29221-2_19

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  • DOI: https://doi.org/10.1007/978-3-319-29221-2_19

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-29220-5

  • Online ISBN: 978-3-319-29221-2

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