Petersburg Department of Steklov Institute of Mathematics

PREPRINT 14/2000


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$k$- $k$-

This preprint was accepted 2000
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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.}


                       
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