This preprint was accepted сентябрь 2000
Contact:
А.В.Пастор
ABSTRACT: We prove that if all vertices of $k$-connected graph~$G$ has degree at least~${k+1}$ then for any minimal fragment~$H$ of~$G$ there is an edge~${(a,b)}$, vere vertex~${a \in H}$, vertex~${b \not\in H}$ and graph~${G-\{(a,b)\}}$ is $k$-connected too.}[ Full text: (.ps.gz)]