References
D. Gusfield, “Connectivity and edge disjoint spanning trees,”Inf. Proc. Lett.,16, 97–99 (1983).
W. H. Cunningham, “Optimal attack and reinforcement of a network,”J. ACM,32, 549–561 (1985).
V. A. Trubin, “Definition of the strength of a graph,”Dokl. Akad. Nauk SSSR,316, No. 1, 1060–1064 (1991).
V. A. Trubin, “Deficiency of network homogeneity and its reduction,”Dokl. Akad. Nauk SSSR,318, No. 1, 43–47 (1991).
V. A. Trubin, “Strength of a network, its reinforcement, and tree packing,”Kibernetika, No. 2, 67–75 (1991).
M. W. Padberg and L. A. Wolsey, “Fractional covers for forests and matchings,”Math. Progr.,29, 1–14 (1984).
G. Gallo, M. D. Grigoriadis, and R. E. Tarjan, “A fast parametric maximum flow algorithm and applications,”SIAM J. Comput.,18, No. 1, 30–55 (1989).
D. Gusfield, “Computing the strength of a graph,”SIAM J. Comput.,20, No. 4, 639–654 (1991).
A. V. Goldberg and R. E. Tarjan, “A new approach to the maximum flow problem,”J. ACM,35, 921–940 (1988).
J. Edmonds, “Edge-disjoint branchings,” in:Combinatorial Algorithms, Algorithmics Press, New York (1972), pp. 91–96.
W. H. Cunningham, “Testing membership in matroid polyhedra,”J. Comb. Theory,36B, No. 2, 161–188 (1984).
R. E. Bixby, O. M.-C. Marcotte, and L. E. Trotter, “Packing and covering with integral feasible flows in integral supply-demand networks,”Math. Progr.,39, No. 3, 231–239 (1987).
P. A. Pevzner, “An efficient algorithm for packing branchings in a weighted graph,” in:Combinatorial Methods in Flow Problems [in Russian], No. 3, VNIISI, Moscow (1987), pp. 113–123.
M. Grotchel, L. Lovasz, and A. Schrijver,Geometric Algorithms and Combinatorial Optimization, Springer, Berlin (1988).
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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 94–99, May–June, 1993.
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Trubin, V.A. Strength of a graph and packing of trees and branchings. Cybern Syst Anal 29, 379–384 (1993). https://doi.org/10.1007/BF01125543
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DOI: https://doi.org/10.1007/BF01125543