Several Conditions For The Existences Of Factors Of Two Types Of Graph

Content: The paper has mainly proved these conclusions in the first and second chapter:(Ⅰ) Let m.d be a positive integer and m ≥ 2 . let G be a [2md+1)- regular multigraph. It is proved that if G does not contain (2m-3)d + 4 cut edges, then G has a 2d - factor. Furthermore, it is shown that the result in this paper is best possible.(Ⅱ) Let n (n≥3 ), a and b be integers, and f(x) be a non-negative integerfunction. Let G be a K1.n - free connected simple graph ( n≥3 ) withΣ f(x) even and 0