A DEGREE CONDITION FOR THE EXISTENCE OF CONNECTED [k, k + 1]-FACTORS  

作　　者：CAI Maocheng (Institute of Systems Science, Academia Sinica,Beijing 100080, China) 

出　　处：《Systems Science and Mathematical Sciences》1995年第4期364-368,共5页

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.

关 键 词：CONNECTED FACTOR MATCHING graph. 

分 类 号：O174[理学—数学]