Induced Nets and Hamiltonicity of Claw-Free Graphs

The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced $$K_{1,3}$$ is hamiltonian if every endvertex of each induced net of G has degree at least $$(|V(G)|-2)/3$$ . In this paper we prove this conjecture in the affirmative.