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

19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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On the optimal rectricted arc-connectivity of digraphs

Presented by Dr. Pedro GARCIA VAZQUEZ
Type: Oral presentation
Track: General session

Content

For a strongly connected digraph $D$ the restricted arc-connectivity $\lambda'(D)$ is defined as the minimum cardinality of an arc-cut over all arc-cuts $S$ satisfying that $D-S$ has a non trivial strong component $D_1$ such that $D-V(D_1)$ contains an arc. In this work we prove that every digraph on at least 4 vertices and of minimum degree at least 2 is $\lambda'$-connected and $\lambda'(D)\le \xi'(D)$, where $\xi'(D)$ is the minimum arc-degree of $D$. Also we introduce the notion of super-$\lambda'$ digraphs and provide a sufficient condition for a $s$-geodetic digraph to be super-$\lambda'$.

Place

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

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