摘要
ＡＤＥＧＲＥＥＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＥＸＩＳＴＥＮＣＥＯＦＣＯＮＮＥＣＴＥＤ［ｋ，ｋ＋１］－ＦＡＣＴＯＲＳＡＤＥＧＲＥＥＣＯＮＤＩＴＩＯＮＦＯＲＴＨＥＥＸＩＳＴＥＮＣＥＯＦＣＯＮＮＥＣＴＥＤ［ｋ，ｋ＋１］－ＦＡＣＴＯＲＳ￥ＣＡＩＭａｏｃｈｅｎ...
The following result is proved in this paper.Let k be an integer > 2 2 and G be a connected graph of order n.If G has a k-factor F and,moreover, among any three independent venices of G there are(at least)two venices with degree sum at least n-k,then G has a matching M such that M and F are edge-disjoint and M + F is a connected [k,k + 1]-factor of G.As immediate consequences,the result gives a solution to a problem and a proof to a conjecture of Kano on the existence of connected [k, k + 1]-factor.
