Bipartite graphs and digraphs with maximum connectivity

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Abstract

Recently, some sufficient conditions for a digraph to have maximum connectivity or high superconnectivity have been given in terms of a new parameter which can be thought of as a generalization of the girth of a graph. In this paper similar results are derived for bipartite digraphs and graphs showing that, in this case, all the known conditions can be improved. As a corollary, it is shown that any bipartite graph of girth g and diameter D ≤ g - 2 (respectively D≤g -1) has maximum vertex-connectivity (respectively maximum edge-connectivity). This implies a result of Plesnik and Znám stating that any bipartite graph with diameter three is maximally edge-connected. © 1996 Elsevier Science B.V.

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Fàbrega, J., & Fiol, M. A. (1996). Bipartite graphs and digraphs with maximum connectivity. Discrete Applied Mathematics, 69(3), 271–279. https://doi.org/10.1016/0166-218X(95)00097-B

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