含有给定k-正则子图的[a,b]-因子

[a,b]-factors Containing a Given k-regular Subgraph

设G是一个图，并设n，k，r，a和b是整数且满足k≥1，k≤a〈b和n≥3．对于G的给定的k-正则图H，如果G是K1，n-free图，且G的最小度至少是那么G有一个[a，b]-因子F使得E（H）∈E（F）．类似地，也得到了关于图G有一个r-因子含有G中给定的k-正则子图的度条件．进一步，指出这些度条件是最佳的．

Let G be a graph, and let n, k, r, a and b be integers such that k ≥ 1, k ≤ a 〈 b and n 〉 3. For given k-regular subgraph H of G, if G is K1,n-free and the minimum degree of G is at least then G has an [a, b]-factor F such that E（H） C E（F）. Similarly, we also obtained a degree condition for graphs to have an r-factor containing a given k-regular subgraph of G. Furthermore, it is shown that the degree conditions are sharp.