Abstract
A graph is (P5,gem)-free, when it does not contain P5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P4) as an induced subgraph. Using a characterization of (P5,gem)-free graphs by their prime graphs with respect to modular decomposition and their modular decomposition trees [6], we obtain linear time algorithms for the following NP-complete problems on (P5,gem)-free graphs: Minimum Coloring, Maximum Weight Stable Set, Maximum Weight Clique, and Minimum Clique Cover. © Springer-Verlag Berlin Heidelberg 2003.
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Bodlaender, H., Brandstädt, A., Kratsch, D., Rao, M., & Spinrad, J. (2003). Linear time algorithms for some NP-complete problems on (P5,gem)-free graphs: (Extended abstract). Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2751, 61–72. https://doi.org/10.1007/978-3-540-45077-1_7
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