Abstract
A graph is ( P 5 ,gem)-free, when it does not contain P 5 (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 P 4 ) as an induced subgraph. We present O ( n 2 ) time recognition algorithms for chordal gem-free graphs and for ( P 5 ,gem)-free graphs. Using a characterization of ( P 5 ,gem)-free graphs by their prime graphs with respect to modular decomposition and their modular decomposition trees [A. Brandstädt, D. Kratsch, On the structure of ( P 5 ,gem)-free graphs, Discrete Appl. Math. 145 (2005), 155–166], we give linear time algorithms for the following NP-complete problems on ( P 5 ,gem)-free graphs: Minimum Coloring; Maximum Weight Stable Set; Maximum Weight Clique; and Minimum Clique Cover.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
