A note on the restricted arc connectivity of oriented graphs of girth four
| Autor: | González-Moreno, D., Ortiz, R. Hernández |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $D$ be a strongly connected digraph. An arc set $S$ of $D$ is a \emph{restricted arc-cut} of $D$ if $D-S$ has a non-trivial strong component $D_{1}$ such that $D-V(D_{1})$ contains an arc. The \emph{restricted arc-connectivity} $\lambda'(D)$ of a digraph $D$ is the minimum cardinality over all restricted arc-cuts of $D$. A strongly connected digraph $D$ is \emph{$\lambda'$-connected} when $\lambda'(D)$ exists. This paper presents a family $\cal{F}$ of strong digraphs of girth four that are not $\lambda'$-connected and for every strong digraph $D\notin \cal{F}$ with girth four it follows that it is $\lambda'$-connected. Also, an upper and lower bound for $\lambda'(D)$ are given. |
| Databáze: | arXiv |
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