二分图中最小度条件与[a,b]-因子的存在性

MINIMUM DEGREE CONDITIONS AND THE EXISTENCE OF[a,b]-FACTORS IN BIPARTITE GRAPHS

设G =(X ,Y ;E)为二分图 ,其中 ｜X｜ =｜Y｜=n .证明了 :若n ≥(a+b) 2b -a+bb 且δ(G) ≥ ana+b,或δ(G) >a+b+n-2 bn+1 ,则G有 [a ,b] 因子 .并且将说明 ,条件δ(G) ≥ aa+bn为最好的 ;而当b<n≤ 4b且bn+1 为整数时 ,δ(G) >a+b+n-2 bn+1 也是最好的 .

It is proved that ,for a balance bipartite graph G=(X,Y;E) where ｜X｜=｜Y｜=n. if n≥(a+b) 2b-a+bb and δ(G)≥ana+b, or δ(G)>a+b+n-2bn+1, then G has an [a,b] factor.It is also shown that the condition δ(G)≥aa+bn is best;when b<n≤4b and bn+1 is an integer, δ(G)>a+b+n-2bn+1 is also best.