【摘要】 设Γk={G||E(G)|-|V(G)|=k且G是至少有3个顶点的H图},Γn,k={G|G是阶为n≥3的图且|E(G)|-|V(G)|=k}.用f(G)表示图G的H圈数.令h(k)=max{f(G)|G∈Γk}和h(n,k)=max{f(G)|G∈Γn,k}.作者得到h(k)的上界和下界,并且当n为大于等于k的奇数以及k≤n2+1时,确定了h(n,k).更多还原

【Abstract】 The set of Hamilton graphs with |E（G）|-|V（G）|=k and at least three vertices is denoted by Γ_k. The set of Hamilton graphs with |E（G）|-|V（G）|=k and n vertices is denoted by Γ_n,k and the number of Hamilton cycles of a graph G is denoted by f（G）. Let h（k）= max {f（G）|G∈Γ_k} and h（n,k）= max {f（G）|G∈Γ_n,k} . In this paper, we get a lower and upper bound of h（k）, and determine h（n,k） when n is an odd with n≥k or k≤n2+1.更多还原