Almost claw‐free graphs
Zdeněk Ryjáček · Journal of Graph Theory · 1994
Abstract We say that G is almost claw‐free if the vertices that are centers of induced claws (K1,3) in G are independent and their neighborhoods are 2‐dominated. Clearly, every claw‐free graph is almost claw‐free. It is shown that (i) every even connected almost claw‐free graph has a perfect matching and (ii) every nontrivial locally connected K1,4‐free almost claw‐free graph is fully cycle extendable.