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The existence theorem of contractible edges in h-connected graphs;

h-连通图中可收缩边的存在定理

The contractible edges of the longest cycle in some 5-connected graphs;

某些5-连通图中最长圈上的可收缩边

Kriesell conjectured that every K, connected graph has a k-contractible edge if the degree sum of any two adjacent vertices is at least 2 5k/4- 1.

Kriesell(2001年)猜想:如果k连通图中任意两个相邻顶点的度的和至少是25k/4-1,则图中有k-可收缩边。

It is proved that any contraction critical 5-connected graph on n vertices has at least n+1 trivially non-contractible edges.

证明n个顶点的收缩临界5连通图中至少有n+1条平凡不可收缩边。

By studying the relationship between <E_C(G)> and edgecut,we draw some characteristies concerning an distribution of contractible edges in an edgecut of a 3-connected graph .

　文章中我们通过研究连通图边割和可缩边导出子图的关系,给出了3连通图边割上可缩连分布的一些性质。

This paper presents a survey on the properties and distributions of contractible edges and removable edges in 3 connected graphs.

综述了３连通图中可缩边和可去边的性质以及它们在图中的分布情形。

Ando proved that in a minimally k-connected graph G which does not contain a K1+C4,if for any vertex x∈V(G) of degree k,there exists and edge incident with x which is not contained any triangle,then G has a k-contractible edge.

Ando证明了如果G是极小的k-连通图,且G中不含有K1+C4,若对于V(G)中的任意一个k度点x,与x关联的边中都存在一条不在三边形中的边,那么G中含有k-可收缩边。