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

T Karthick,Frédéric Maffray

doi:10.1007/978-3-319-42634-1_31

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

T Karthick, Frédéric Maffray

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

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Publication Date: Jan 1, 2016

Citations: 4

Affiliation: Indian Statistical Institute, Laboratoire des Sciences pour la Conception, l'Optimisation et la Production, French National Centre for Scientific Research, Université Grenoble Alpes

#Maximum Weight Independent Set Problem #Maximum Weight Independent Set + Show 8 more

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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$.

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