A graph is claw-free iff it does not contain the complete bipartite graph K_(1, 3) (known as the "claw graph"; illustrated above) as a forbidden induced subgraph. The line graph of any graph is claw-free, as is the complement of any triangle-free graph. Classes of graphs that are claw-free include 1. antiprism graphs, 2. barbell graphs, 3. bishop graphs (and their connected components), 4.

claw graph | complete bipartite graph | forbidden induced subgraph | line graph | perfect matching