Abstract :
A graph G is quasi claw-free if it satisfies the property: d(x, y) = 2 ⇒ there exists u ϵ N(x) ∩ N(y) such that N[u]⊂ N[x]∪ N[y]. This property is satisfied if in particular u does not center a claw (induced K1,3). Many known results on claw-free graphs, dealing with matching and hamiltonicity are extended to the larger class of quasi-claw-free graphs.
