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- Q5129750 subject Q7012142.
- Q5129750 subject Q7217193.
- Q5129750 abstract "In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph.A claw is another name for the complete bipartite graph K1,3 (that is, a star graph with three edges, three leaves, and one central vertex). A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph.Claw-free graphs were initially studied as a generalization of line graphs, and gained additional motivation through three key discoveries about them: the fact that all claw-free connected graphs of even order have perfect matchings, the discovery of polynomial time algorithms for finding maximum independent sets in claw-free graphs, and the characterization of claw-free perfect graphs. They are the subject of hundreds of mathematical research papers and several surveys.".
- Q5129750 thumbnail Complete_bipartite_graph_K3,1.svg?width=300.
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- Q5129750 wikiPageExternalLink gc_62.html.
- Q5129750 wikiPageExternalLink spgc.pdf.
- Q5129750 wikiPageExternalLink claw.pdf.
- Q5129750 wikiPageExternalLink claws_survey.pdf.
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- Q5129750 comment "In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph.A claw is another name for the complete bipartite graph K1,3 (that is, a star graph with three edges, three leaves, and one central vertex). A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern.".
- Q5129750 label "Claw-free graph".
- Q5129750 depiction Complete_bipartite_graph_K3,1.svg.