[a,b]-对等图的范-型条件  

Fan-type Results for the Existence of [a,b]-Uniform Graphs

作　　者：刘红霞[1,2] 高敬振[3] 

机构地区：[1]山东大学数学院,济南250100 [2]烟台大学数学与信息科学院,烟台264005 [3]山东师范大学数学院,济南250014

出　　处：《大学数学》2009年第4期116-121,共6页College Mathematics

基　　金：烟台大学青年基金项目(SX07211)

摘　　要：既是[a,b]-覆盖又是[a,b]-消去的图称为[a,b]-对等图.设1≤a<b为整数,G是阶为n的图,其中n相对于a,b充分大.若δ(G)≥a+1且对G中每一对满足d(x,y)=2的顶点x,y,都有max{degG(x),degG(y)}>an+1a+b,则G为[a,b]-对等图.给出了一个图是[a,b]-对等图的关于范-型条件及邻域并的若干充分条件,并指出定理中的条件在一定意义上是最好可能的.Both [a,b]-covered and [a,b]-deleted graphs are [a,b]-uniform graphs.Let 1≤a＆lt;b be integers and G a graph of order n sufficiently large for a and b.Then G is [a,b]-uniform if the minimum degree is at least a＋1 and for any two vertices x and y of G such that d（x,y）=2,max{degG（x）,degG（y）}〉an＋1/a＋b.Several sufficient conditions about Fan-type condition and neighborhood union for graphs to be [a,b]-uniform are given.Furthermore,we show that the results in this paper are best possible in some sense.

关 键 词：图 范型-条件 [A B]-因子 [a b]-对等图 邻域并 

分 类 号：O157.5[理学—数学]