线图中2-因子分支数一些结果的改进

The Improvement of Some Results of the Components of 2-Factors in Line Graph

设G为一简单图,该文重点研究了图及其补图的线图中2-因子的分支数,改进了Nebesk■的一个结果,得出如下结论:阶数n≥5的简单图G,G和L(G)分别是G的补图和线图,存在一个图G′∈{G,■},线图L(G′)包含k个分支的2-因子,其中k=1,…,└(n-3)/4」.讨论了图及其补图的线图中2-因子分支的最大个数的界的问题,并给出了线图中存在一定分支数的2-因子的Chvtáal-Erds型条件,即对于阶为n的图G,如果k(G)≥a(G)-1,则L(G)中存在所有k个分支的2-因子,其中1≤k≤└n^(1/2)/3」.

Let G be a simple graph（n≥5）,G-be the complement of G and L（G） be the line graph of G;then there exists a graph G′∈{G,G^-} such that L（G′） contains a 2-factor with k cycles for all k,1≤k≤[（n-3）/4] which extends an known result of Nebesk.We also give a Chvátal-Erds condition for the existence of 2-factor with some special number of components： if k（G）≥a（G）-1 then L（G） contains a 2-factor with cycles for all k,1≤k≤[/n/3」.