r-正则图为k-消去图的充分条件  

SUFFICIENT CONDITIONS FOR rREGULAR GRAPHS TO BE kDELETED

作　　者：吴强[1] 

机构地区：[1]山东工业大学数理系

出　　处：《山东工业大学学报》1998年第1期6-10,共5页

摘　　要：主要研究了正则图中的ｋ－消去图与图的边连通度之间的关系，从而推广了Ｂｏｌｏｂáｓ的结果．其结果如下：Ⅰ设Ｇ是一个ｒ－正则图，｜Ｖ（Ｇ）｜为偶数，λ（Ｇ）≥２．若ｋ为一整数，且ｒ／λ≤ｋ≤ｒ－ｒ／λ，则Ｇ为ｋ－消去图．Ⅱ设ｒ和ｋ为偶数，２≤ｋ≤ｒ，则每一个ｒ－正则图都为ｋ－消去图．Ⅲ设Ｇ为ｒ－正则图，λ（Ｇ）＝λ≥２，且λ＊＝２［λ／２］＋１．若ｒ为奇数，ｋ为偶数，且使得２≤ｋ≤ｒ－ｒ／λ＊，则Ｇ为ｋ－消去图．In this paper,we study relations between kdeleted graph and edge connectivity of regular graph and generalize Bollobás results.The main results are the following theorems:Theorem I.Let G be an rregular graph such that |V(G)| is even and λ(G)≥2.If k is an integer and r/λ≤r-r/λ then G is a kdeleted graph.Theorems Ⅱ:Let r and k be even integers,2≤k≤r.Then every rregular graph is a kdeleted graph.Theorems Ⅲ:Let G be a rregular graph with λ(G)=λ≥2 and λ*=2+1.If r is odd and k is even such that 2≤k≤r-r/λ* then G is a kdeleted graph.

关 键 词：正则图 因子 子集 /消去图 边连通度 

分 类 号：O157.5[理学—数学]