×

zbMATH — the first resource for mathematics

Blocking and anti-blocking pairs of polyhedra. (English) Zbl 0254.90054

MSC:
90C35 Programming involving graphs or networks
90C10 Integer programming
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] C. Berge, ”Färbung von Graphen, deren sämtliche bzw deren ungerade Kreise starr sind (Zusammenfassung),”Wiss. Z. Martin-Luther-Univ. Halle Wittenberg Math. Natur. Reihe (1961) 114.
[2] C. Berge, ”Some classes of perfect graphs,” in:Graph theory and theoretical physics, Ed. F. Harary (Academic Press, New York, 1967). · Zbl 0203.26403
[3] C. Berge, ”The rank of a family of sets and some applications to graph theory,” in:Recent progress in combinatorics, Ed. W.T. Tutte (Academic Press, New York, 1969). · Zbl 0197.50402
[4] R.P. Dilworth, ”A decomposition theorem for partially ordered sets,”Annals of Mathematics 51 (1950) 161. · Zbl 0038.02003 · doi:10.2307/1969503
[5] R.J. Duffin, ”The extremal length of a network,”J. Math. Anal. Appl. 5 (1962) 200. · Zbl 0107.43604 · doi:10.1016/S0022-247X(62)80004-3
[6] J. Edmonds, ”Paths, trees and flowers,”Canadian Journal of Mathematics 17 (1965) 499. · Zbl 0132.20903 · doi:10.4153/CJM-1965-045-4
[7] J. Edmonds, ”Maximum matching and a polyhedron with (0, 1)-vertices,”J. Research National Bureau of Standards 69B (1965) 125. · Zbl 0141.21802
[8] J. Edmonds, ”Minimum partition of a matroid into independent sets,”J. Research National Bureau of Standards 69B (1965) 67. · Zbl 0192.09101
[9] J. Edmonds, ”Lehman s switching game and a theorem of Tutte and Nash-Williams,”J. Research National Bureau of Standards 69B (1965) 73. · Zbl 0192.09102
[10] J. Edmonds, ”Matroids and the greedy algorithm” (lecture, Princeton, August 1967). · Zbl 0253.90027
[11] J. Edmonds, ”Optimum branchings,” in:Mathematics of the decision sciences, Lectures in applied mathematics, Eds. G.B. Dantzig and A.F. Veinott, Jr., Vol. 11 (American Mathematical Society, 1968) p. 346. · Zbl 0198.52605
[12] J. Edmonds, ”Submodular functions, matroids, and certain polyhedra,” in:Combinatorial structures and their applications, Eds. R. Guy, H. Hanani, N. Sauer, J. Schonheim (Gordon and Breach, 1970) p. 69. · Zbl 0268.05019
[13] J. Edmonds, ”Edge-disjoint branchings” (to appear). · Zbl 0198.52605
[14] J. Edmonds and D.R. Fulkerson, ”Bottleneck extrema,”J. Combinational Theory 8 (1970) 299. · Zbl 0218.05006 · doi:10.1016/S0021-9800(70)80083-7
[15] L.R. Ford, Jr., and D.R. Fulkerson,Flows in networks (Princeton University Press, 1962). · Zbl 0106.34802
[16] D.R. Fulkerson, ”The maximum number of disjoint permutations contained in a matrix of zeros and ones,”Canadian Journal of Mathematics 16 (1964) 729. · Zbl 0123.00302 · doi:10.4153/CJM-1964-069-0
[17] D.R. Fulkerson, ”Networks, frames, blocking systems,” in:Mathematics of the decision sciences, lectures in applied mathematics, Eds. G.B. Dantzig and A.F. Veinott, Jr., (American Mathematical Society, 1968) p. 303. · Zbl 0182.53402
[18] D.R. Fulkerson, ”Blocking polyhedra,” in:Graph theory and its applications, Ed. B. Harris (Academic Press, 1970) p. 93. · Zbl 0217.18505
[19] D.R. Fulkerson, ”Anti-blocking polyhedra,” to appear inJ. Combinational Theory. · Zbl 0227.05015
[20] D.R. Fulkerson, ”Disjoint common partial transversals of two families of sets,” in:Studies in pure mathematics, Ed. L. Mirsky (Academic Press, 1971) p. 107. · Zbl 0216.29802
[21] T.C. Hu, ”Multi-commodity network flows,”Operations Research 11 (1963) 344. · Zbl 0123.23704 · doi:10.1287/opre.11.3.344
[22] E.L. Lawler, ”Optimal matroid intersections,” in:Combinatorial structures and their applications, Eds. R. Guy, H. Hanini, N. Sauer, J. Schonheim (Gordon and Braech, 1970) p. 233.
[23] A. Lehman, ”On the width length inequality,” Mimeo. (1965). · Zbl 0418.90040
[24] J.T. Robacker,Min-max theorems on shortest chains and disjunct cuts of a network (The Rand Corporation, RM-1660-PR, 1956).
[25] W.T. Tutte, ”On the problem of decomposing a graph inton connected factors.”J. London Mathematical Society 36 (1961) 221. · Zbl 0096.38001 · doi:10.1112/jlms/s1-36.1.221
[26] W.T. Tutte, ”Lectures on matroids,”J. Research National Bureau of Standards 69B (1965) 1. · Zbl 0151.33801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.