圈和分数[a,b]-因子

Cycles and Fractional [a,b]-Factors

设1≤a,a+2≤b是整数.设G是一个具有圈C的图,且其阶|G|≥(a+b)(2a+b+1)／b.当δ(G)≥a+2且max{dG(x),dG(y)}≥a|G|／(a+b)+2对每一对G中不相邻的两点x和y都成立.那么G有一个分数[a,b]-因子F使得E(F)∩E(C)=(?).这个度条件下的下界是紧的.作为推论,我们得到具有哈密顿圈C的图有一个[a,b]-因子F使得E(C)(?)E(F)的一个度条件.

Let 1≤a,a+2≤b be intergers. Let G be a graph with a cycle C and of order (?) G (?)≥(a+b)(2a+b+1)/ b . Suppose thatδ(G)≥a+2 and max (?) dG(x) ,dG(y) ≥a|G|/(a+b)+2 for each pair of nonadjacent vertices x and y in G . Then G has a fractional [a,b] - factor F such that E(F)∩E(C)=(?). The lower bound on the degree condition is sharp. As consequences, we obtain the degree conditions for a graph with a Hamiltonian cycle C to have a [a ,b] - factor Fsuch that E(C)(?)E(F)