Hamiltonicity of 2-connected quasi-claw-free graphs

Abstract

A graph G is called quasi-claw-free if it satisfies the property: d ( x , y )=2 ⇒ there exists u ∈ N ( x )∩ N ( y ) such that N [ u ]⊆ N [ x ]∪ N [ y ]. Let G be a 2-connected quasi-claw-free graph of order n. If δ ( G )⩾ n /4, then G is hamiltonian or G∈ F , where F is a family of nonhamiltonian graphs of connectivity 2.