关于图中存在不含给定k-因子的[a,b]-因子的度条件  

DEGREE CONDITIONS FOR GRAPHS TO HAVE [a,b]-FACTORS EXCLUDING A GIVEN k-FACTORS

作　　者：李建湘[1] 汤四平[1] 

机构地区：[1]湖南科技大学数学院,湘潭411201

出　　处：《系统科学与数学》2009年第8期1052-1060,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题

摘　　要：设1(?)a<b,0(?)k是整数.设G是一个含有k-因子Q且阶为|G|的图.设δ(G)表示G的最小度,且δ(G)(?)a+k.如果Q连通,设ε=k.否则设ε=k+1.证明:当b(?)a+ε-1时,如果对G的任意两个不相邻的点x和y都有max{d_G(x),d_G(y)}(?)max{(a|G|)/(a+b),(|G|+(a-1)(2a+b+ε-2))/(b+1)}+k,那么G有一个[a,b]-因子F使得E(F)∩E(Q)=(?).这个度条件是最佳的,条件b(?)a+ε一1不能去掉.进一步,得到图存在含给定k-因子的|a,b|-因子的度条件.Let 1≤a〈b,1≤k be integers. Let G be a graph of order │G│ with a k-factor Q. Suppose that δ（G）≥a＋k.and max {dG（x）,dG（y）}≥max{a│G│/a＋b,（│G│＋（a-1）（2a＋b＋ε-2））/b＋1}＋k for each pair of nonadjacent vertices x and y in G, where ε = k if Q is connected, otherwise ε = k ＋ 1. Then G has an [a,b]-factor F such that E（F）∩E（Q）=Ф.The lower bound on the degree condition is sharp and the condition b≥a＋ε-1 can not be deleted. As consequences,the degree conditions are obtained for a graph with a k-factor Q to have [a,b]-factor F such that E（Q） E（F）.

关 键 词：图 因子 [A B]-因子 K-因子 度条件. 

分 类 号：O157.5[理学—数学]