关键词: 　图论, ［a,b］-因子, 邻域并．

Abstract:

Let a≤b be integers and G a graph. A spanning subgraph F of G is called an [a,b] factor of G if a≤d_F(v)≤b for all v∈V(G). A sufficient condition concerning neighborhood unions for the existence of an [a,b] factor in a graph is given. The author prove the following result: Let a<b be integers and G a graph of order n such that n>(a+b)(2a+2b-3)/b. Assume |N_G (u)∪N_G (v)|≥an/(a+b), for each pair of nonadjacent vertices u,v in G and the minimum degree is at least a, Then G has an [a,b] factor.

Key words: Ｇｒａｐｈ, ［a,b］-ｆａｃｔｏｒ, Ｎｅｉｇｈｂｏｒｈｏｏｄｕｎｉｏｎ．