图有不含匹配的[a,b]—因子的邻域条件

The neighborhood condition for graphs to have [ a, b ] - factors containing no an matching

设G是一个n阶图，a和b是整数使得1≤a<b，设H是G的具有m条边的匹配，δ（G）是最小度，证明了：若δ（G）≥a+1,n≥2(a+b)(a+b-1)/b,并且对G的任意两个不相邻的点x和y都有|NG(x)∪y)|≥an/(a+b)+2，则G有[a,b]-因子F使得E（H）∩E（F）=φ。

Let G be a graph of order n ,and let aand bbe integers such that 1≤a<b.Let H be any matching of G wiht m edges,and δ(G) be the minimum degree.Then we prove that if δ(G)≥a+1,n≥2(a+b)(a+b-1)/b,and |N G(x)∪N G(y)|≥an/(a+b)+2 for any two non-adjacent vertices x and y of G,then G has an -factor F such that E(H)∩E(F)=.