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Maximum Weight Independent Sets in (\(S_{1,1,3}\), bull)-free Graphs

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Computing and Combinatorics (COCOON 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9797))

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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. The MWIS problem is well known to be NP-complete in general, even under substantial restrictions. The computational complexity of the MWIS problem for \(S_{1, 1, 3}\)-free graphs is unknown. In this note, we give a proof for the solvability of the MWIS problem for (\(S_{1, 1, 3}\), bull)-free graphs in polynomial time. Here, an \(S_{1, 1, 3}\) is the graph with vertices \(v_1, v_2, v_3, v_4, v_5, v_6\) and edges \(v_1v_2, v_2v_3, v_3v_4, v_4v_5, v_4v_6\), and the bull is the graph with vertices \(v_1, v_2, v_3, v_4, v_5\) and edges \(v_1v_2, \) \( v_2v_3, v_3v_4, \) \( v_2v_5, v_3v_5\).

F. Maffray—Partially supported by ANR project STINT under reference ANR-13-BS02-0007.

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Authors and Affiliations

  1. Indian Statistical Institute, Chennai Centre, Chennai, 600113, India

    T. Karthick

  2. CNRS, Laboratoire G-SCOP, University of Grenoble-Alpes, Grenoble, France

    Frédéric Maffray

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  1. T. Karthick
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  2. Frédéric Maffray
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Correspondence to T. Karthick .

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Editors and Affiliations

  1. Virginia Commonwealth Univ , Richmond, Virginia, USA

    Thang N. Dinh

  2. University of Florida , Gainesville, Alabama, USA

    My T. Thai

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Karthick, T., Maffray, F. (2016). Maximum Weight Independent Sets in (\(S_{1,1,3}\), bull)-free Graphs. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_31

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  • DOI: https://doi.org/10.1007/978-3-319-42634-1_31

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-42634-1

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