关于哈密顿线图的一个注记

A Note on Hamiltonian Line Graphs

e=uv是图G的任意一边,其中d(u)和d(V)分别是顶点u和v的度数。本文证明了以下结论:设G是p≥4阶简单图,且至 少有三务边,若G不是长度为3的道路,且对任何两务无公共顶点的边e0及e1,d(e0)+d(e1)≥2p-2,则G的线图L(G)有哈密顿圈。

For each edge e=uv of a simple graph G, let d(e) =d(u) and d(v) are the degrees of the vertiees u and v respeevively Let G be a simple graph with p≥4 vertiees and at least 2 edges. If G is not a path of length 3 and for each pair of edges e0 and el which have no common vertex, d(e0)+d(e1) ≥2p-2, then the line graph L(G) of G has a Hamiltonian style.