3-Restricted arc connectivity of digraphs |
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Authors: | Shangwei Lin Ya’nan Jin Chunfang Li |
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Institution: | 1. School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China;2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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Abstract: | The -restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset of a strong digraph is a -restricted arc cut if has a strong component with order at least such that contains a connected subdigraph with order at least . The -restricted arc connectivity of a digraph is the minimum cardinality over all -restricted arc cuts of .Let be a strong digraph with order and minimum degree . In this paper, we first show that exists if and, furthermore, if , where is the minimum 3-degree of . Next, we prove that if . Finally, we give examples showing that these results are best possible in some sense. |
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Keywords: | Network Digraph Connectivity Minimum degree |
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