图有[a,b]因子的邻域条件

不含有图K1，R的图称为K1,r-free图，设G是一个具有顶点集V（G）的图，设n(≥3),a和b是整数，使得b≥a≥1，若b是奇数，设b≥n-1。我们证明了每个连通的K1,r-free图G在b|V(G)|为偶数，它的最小度至少是a n-1,|V(G）≥ （2(a b)-1)(a b-1)/b，以及|NG(x）∪NG（y)|≥a|V(G)|a b对V的任意两个不邻接的点x和y都成立时，G有一个a,b]因子。

A Neighborhood Condition for Graphs to have [a,b]-Factors

A graph is called K1,n-free if it contains no K1,n as an induced subgraph. Let G be a graph with vertex set V(G). Let n(≥3), a and b be integers such that b≥a≥1, and if b is odd, bn-1. We prove that every K1,n-free connected graph G with b|V(G)|even has an a,b]-factor if its minimum degree is at least a+n-1, |V(G)|≥(2(a+b)-1)(a+b-1)/b, and|NG(x)∪NG(y)|≥(a|V(G)|)/(a+b)for any two non-adjacent vertices x and y of V(G).