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- W2614363579 abstract "Let k be a positive integer, and D = (V(D), E(D)) be a minimally k-edge-connected simple digraph. We denote the outdegree and indegree of x ∈ V(D) by δD(x) and ρD(x), respectively. Let u+(D) denote the number of vertices x in D with δD(x) = k, ρD(x) > k; u±(D) the number of vertices x with δD(x) = ρD(x) = k; u− (D) the number of vertices x with δD(x) > k, ρD(x) = k. W. Mader asked the following question in [Mader, in Paul Erdös is Eighty, Keszthely, Budapest, 1996]: for each k ≥ 4, is there a ck > 0 such that u+(D) + 2u±(D) + u−(D) ≥ ck|D| holds? where |D| denotes the number of the vertices of D. In this article, we give a partial result for the question. It is proved that, for |D| ≥ 2k − 2, © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 94–108, 2000" @default.
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- W2614363579 date "2000-02-01" @default.
- W2614363579 modified "2023-09-26" @default.
- W2614363579 title "The number of vertices of degreek in a minimallyk-edge-connected digraph" @default.
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- W2614363579 doi "https://doi.org/10.1002/(sici)1097-0118(200002)33:2<94::aid-jgt4>3.0.co;2-i" @default.
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