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1989•Journal of Graph TheoryRequires access

On critically connected digraphs

W. Mader

Open publisher page 5 citations

Abstract

Abstract A digraph is called critically connected if it is connected, but the deletion of any vertex destroys the connectivity. We prove that every critically connected finite digraph has at least two vertices of outdegree one. As an application, we show that for n ≧ 2, there is no n‐connected, non‐complete, finite digraph such that the deletion of any n vertices results in a disconnected digraph.

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What this paper is about

Abstract A digraph is called critically connected if it is connected, but the deletion of any vertex destroys the connectivity. We prove that every critically connected finite digraph has at least two vertices of outdegree one. As an application, we show that for n ≧ 2, there is no n‐connected, non‐complete, finite digraph such that the deletion of any n vertices results in a disconnected digraph.

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Available abstract

Abstract A digraph is called critically connected if it is connected, but the deletion of any vertex destroys the connectivity. We prove that every critically connected finite digraph has at least two vertices of outdegree one. As an application, we show that for n ≧ 2, there is no n‐connected, non‐complete, finite digraph such that the deletion of any n vertices results in a disconnected digraph.

Key concepts: Digraph, Combinatorics, Vertex (graph theory), Strongly connected component, Mathematics, Vertex connectivity, Discrete mathematics, Graph

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