哈密顿线图中2-因子的分支数

The Components of 2-factors in Hamiltonian Line Graphs

设G为一简单图,本文证明了:如果G的线图L(G)为哈密顿的,且在G中存在两个顶点u、υ∈V(G),满足d(u)+d(v)f(n)(f(n)为整数),那么L(G)中存在k个分支的2-因子,其中1 k﹂f(n4)-2」,且说明了当f(n)n时所给的结果为最好可能的,这个结果是对R.J.Gould和E.A.Hynds[4]的结果的推广和加强.

Let be a simple graph,In this paper the author showed that: If L(G) which is the Line Graph of G is Hamiltonian and there exist two vertices u,v∈V(G) in G,such that d(u)+d(v)f(n)(f(n) is a positive integer),then L(G) has a 2-factor with k components(1kf(n)-24) and this result is best possible when f(n)n.This result is an extension and strength of R.J.Gould and E.A.Hynds[4]'s result.