A PROOF OF BROERSMA AND VELDMAN'S CONJECTURES
Zhiquan Hu · 1996
Let F be a unique graph with degree sequence(1, 1, 1,3,3, 3). The pendent vertices of F are given by a1, a2 and a3. We say a subgraph H of G satisfies property(u,v) if(N(u) ∩ N(v)) - V(H) ≠ . In [1], Broersma and Veldman conjectured that if G is a 2-connected K1,3-be graph and if every induced F of G satisfies ((a1, a2) and 4(a1, a3)) or ((a1, a2) and 4(2, Q3)) or ((a1, a3) and (a2, a3)), then G is hamiltonian.In this paper,we show that this conjecture is true. This result generalizes an earlier work Of Duffus, Gould and Jacobson. It is (ho) applicable to the showing of the hamiltofority of K1,3-free graphs with low edge density and few degrees.