2-连通图过指定边的长圈(英文)

Large Cycles Passing Through a Specified Edge in 2-connected Graphs

对2 连通非完全图G,令μ(G)=min{max{dG(u),dG(v)}dG(u,v)=2}.一个著名的范定理:每一个2 连通非完全图G包含长至少为min{V(G),2μ(G)}的圈.在这篇论文中我们证明了:若G是2 连通无三角形图,则通过G的任一边存在长至少为min{V(G),2μ(G)}的圈.

For a 2connected noncomplete graph G,let μ(G)=min{max{d(u),d(v)}d(u,v)=2}.A well known Fan Theorem claims that for each 2connected noncomplete graph G,there exists a cycle of length≥min{V(G),2μ(G)} in G.In this paper,we prove the following result : Suppose G is a 2 connected trianglefree graph.Then through each edge of G there exists a cycle of length≥min{V(G),2μ(G)}.