Petersburg Department of Steklov Institute of Mathematics

PREPRINT 14/2000

ןג ץהבלומיי עוגוע ית $k$-ףקסתמןחן חעבזב גות נןפועי $k$-ףקסתמןףפי

This preprint was accepted ׃ֵ־װֲׁׂ״ 2000
Contact: ב.ק.נֱ׃װֿׂ

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.}