【摘要】 设G是一个n阶3-连通图,周长为C(G),独立数为,若G是1-坚韧的,且,则G的每一个最长圈是控制圈且;又若G是5/3-坚韧的或,则G是Hamilton图。更多还原

【Abstract】 A number of results are established about long cycles in tough graphs with high degree sums. Let G be a 3-connected graph of order n with circumference c, independence number a and toughness r such that d(x)+d(y)+d(z)+d(w)≥s for all tetrads of independent vertices x, y, z, w. If τ≥1 and s≥ n+c/2, then every longest cycle in G is a dominating cycle and c≥min{n, n + s/4 -α}. Furthermore, when s≥n+(n -1)/2, if τ≥5/3 or δ≥a, then G is hamiltonian.更多还原