图有特殊[a,b]-因子的邻域条件(英文)

The neighborhood conditions for graphs to have special-factors

设G是一个n阶图.设1≤a≤b是整数.设H1和H2是G的任意两个边不交子图,它们分别具有m1和m2条边,以及δ(G)表示最小度.证明:若δ(G)≥a+m2,n≥2(a+b-m1)(a+b-m1-1)/(b-m1),a≤b-(m1+m2),并且|NG(x)∪NG(y)|≥an/(a+b-m1)+2m2对任意两个不相邻的顶点x和y成立,那么G有[a,b]-因子F使得E(H1) E(F)和E(H2)∩E(F)= .

Let G be a graph of order n,and let a and b be integers such that 1≤a≤b.Let H1 and H2 be any two subgraphs of G with m1 edges and m2 edges, respectively,and δ(G) be the minimum degree.Then we prove that if δ(G)≥a+m2,n≥2(a+b-m1)(a+b-m1-1)/(b-m1),a≤b-(m1+m2) and |NG(x)∪NG(y)|≥an/(a+b-m1)+2m2 for any two nonadjacent vertices x and y of G,then G has an factor F such that E(H1)E(F) and E(H2)∩E(F)=.