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

  • T. KarthickEmail author
  • Frédéric Maffray
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


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 \(v_1v_2, \) \( v_2v_3, v_3v_4, \) \( v_2v_5, v_3v_5\).


Graph algorithms Weighted independent set Modular decomposition Claw-free graph Fork-free graph Bull-free graph 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Indian Statistical InstituteChennaiIndia
  2. 2.CNRS, Laboratoire G-SCOPUniversity of Grenoble-AlpesGrenobleFrance

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