关键词: 可收缩边, 最长圈, 5-连通

Abstract: Contractible edge issue plays an important role in the research on graph structure and the proof of some graph properties. We present the distribution of the contractible edges in some longest cycles of 5-connected graphs and address their classification with tree structure theory. Our conclusion is that at least three contractible edges exist on some longest cycles of 5-connected graphs.

Key words: 5-connected, contractible edge, the longest cycle