# Bled'11 - 7th Slovenian International Conference on Graph Theory

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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# Minimally restricted 2-edge connected graphs

Presented by Dr. Juan Carlos VALENZUELA
Type: Oral presentation
Track: General session

## Content

For a connected graph $G$ an edge set $S$ is a restricted edge cut if $G-S$ is disconnected and there is no isolated vertices in $G-S$. The number of edges in a restricted edge cut of minimum cardinality is known as the restricted edge connectivity of $G$, denoted by $\lambda' (G)$. A restricted edge connected graph is minimally restricted $2$-edge connected if $\lambda' (G) = 2$ and $\lambda'(G-e) =1$, for every edge $e\in E(G).$ In this work we study some structural properties of minimally restricted $2$-edge connected graphs. Moreover, we give a necessary and sufficient condition for a $\lambda'$-connected graph $G$ with vertex connectivity $\kappa(G)=2$ to be minimally restricted $2$-edge connected.

## Place

Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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