A Sufficient Condition for Hamiltonicity in 2-Tough Graphs
Let t be a nonnegative real number.The graph G is said to be t-tough if |S| ≥t·c(G-S)with c(G-S)≥ 2 for each vertex set S.The toughness is the largest real number t satisfying the above condition.Let G be a 2-tough graph on n ≥ 3 vertices.If it holds that max{d(u),d(v)}＞n/3+2 for any two nonadjacent vertices u,v ∈ V(G),then G is Hamiltonian.
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