Abstract.
Let D=(V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V|≥f(k) implies |E|≤2k(|V|−k). We also determine the extremal graphs whose size attains this upper bound.
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Basic Research in Computer Science, funded by the Danish National Research Foundation.
Supported by the MTA-ELTE Egerváry Research Group on Combinatorial Optimization, and the Hungarian Scientific Research Fund grant No. F034930, T037547, and FKFP grant No. 0143/2001. Part of this research was done when the second author visited BRICS, University of Aarhus, Denmark.
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Berg, A., Jordán, T. Minimally k-Edge-Connected Directed Graphs of Maximal Size. Graphs and Combinatorics 21, 39–50 (2005). https://doi.org/10.1007/s00373-004-0588-6
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DOI: https://doi.org/10.1007/s00373-004-0588-6