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

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,■} 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 Chvatal-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~(1/2)/3」.