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

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

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.

It is Thomassen who firstly asked if there is a polynomial bounded algorithm for finding a shortest contractible cycle,a shortest separating cycle and a shortest two sided cycle in an embedded graphs.