Minimal claw-free graphs
Peter Dankelmann, Henda C. Swart, Paul van den Berg, Wayne Goddard, Michael D. Plummer · Czechoslovak Mathematical Journal · 2008
A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K 1,3 (claw) as an induced subgraph and if, for each edge e of G, G ™ e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.