Edge-connectivity of undirected and directed hypergraphs

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132 Bibliography [11] E. Cheng, Edge-augmentation of hypergraphs, in: Connectivity Augmentation of Net- works: Structures and Algorithms, Mathematical Programming (ed. A. Frank), Ser. B, Vol. 84, No. 3 (1999), 443–465. [12] B. Cosh, B. Jackson, Z. Király, Local connectivity augmentation is NP-complete, ap- peared in: B. Cosh: Vertex splitting and connectivity augmentation in hypergraphs, Ph.D. thesis, Goldsmiths College, University of London (2000). [13] J. Edmonds, Minimum partition of a matroid into independent sets, J. Res. Nat. Bur. Standards Sect. 869 (1965), 67–72. [14] J. Edmonds, Edge-disjoint branchings, in: B. Rustin, ed., Combinatorial Algorithms (Acad. Press, New York, 1973) 91–96. [15] J. Edmonds, Submodular functions, matroids, and certain polyhedra, in: R. Guy, H. Hanani, N. Sauer, and J. Schönheim (eds.): Combinatorial Structures and their Applications. Gordon and Breach, New York (1970), 69–87. [16] J. Edmonds, Existence of k-edge-connected ordinary graphs with prescribed degrees, J. Res. Nat. Bur. Standards Sect. B 68B (1964), 73–74. [17] J. Edmonds, R. Giles, A min-max relation for submodular functions on graphs, Ann. Discrete Math. 1 (1977), 185–204. [18] L.P. Eswaran, R.E. Tarjan, Augmentation problems, SIAM J. Computing 5 No. 4 (1976), 653–665. [19] B. Fleiner, Detachment of vertices preserving edge-connectivity, SIAM J. Discrete Math., to appear. [20] T. Fleiner, T. Jordán, Coverings and structure of crossing families, in: Connectivity Augmentation of Networks: Structures and Algorithms, Mathematical Programming (ed. A. Frank), Ser. B, Vol. 84, No. 3 (1999), 505–518. [21] L.R. Ford, D.R. Fulkerson, Flows in Networks, Princeton Univ. Press, Princeton NJ., 1962. [22] A. Frank, On the orientation of graphs, J. Combinatorial Theory B 28 No. 3 (1980), 251–261. [23] A. Frank, Finding feasible vectors of Edmonds-Giles polyhedra, Journal of Combina- torial Theory Series B 36 (1984), 221–239.
Bibliography 133 [24] A. Frank, Connectivity augmentation problems in network design, in: J.R. Birge, K.G. Murty (eds.): Mathematical Programming: State of the Art. Univ. of Michi- gan (1994), 34–63. [25] A. Frank, Orientations of graphs and submodular flows, Congressus Numerantium 113 (1996), 111–142. [26] A. Frank, Matroids and submodular functions, in: Annotated Bibliographies in Com- binatorial Optimization (M. Dell’Amico, F. Maffioli, S. Martello, eds.), 1997, John Wiley, 65–80. [27] A. Frank, On disjoint trees and arborescences, in: Algebraic Methods in Graph Theory, Colloquia Mathematica Soc. J. Bolyai 25, North Holland (1978), 159–169. [28] A. Frank, Kernel systems of directed graphs, Acta Sci. Math. (Szeged) 41, 1-2 (1979), 63–76. [29] A. Frank, Augmenting graphs to meet edge-connectivity requirements, SIAM J. Discrete Math. 5 No. 1 (1992) 22–53. [30] A. Frank, On a theorem of Mader, Annals of Discrete Mathematics 101 (1992) 49–57. [31] A. Frank, Z. Király, Graph orientation with edge-connection and parity constraints, Combinatorica 22 (2002), 47–70. [32] A. Frank, É. Tardos, Generalized polymatroids and submodular flows, Mathematical Programming, Ser. B, Vol. 42 (1988), 489–563. [33] A. Frank, T. Jordán, Z. Szigeti, An orientation theorem with parity conditions, Dis- crete Applied Mathematics 115 (2001), 37–45. [34] A. Frank, L. Szegő, Constructive characterizations for packing and covering with trees, Discrete Applied Mathematics, to appear [35] A. Frank, T. Király, Combined connectivity augmentation and orientation problems, Discrete Applied Mathematics, to appear [36] A. Frank, T. Király, Z. Király, On the orientation of graphs and hypergraphs, Discrete Applied Mathemathics, to appear [37] A. Frank, T. Király, M. Kriesell, On decomposing a hypergraph into k connected sub- hypergraphs, Discrete Applied Mathematics, to appear
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Edge-connectivity of undirected and
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4 Contents 6 Hypergraph orientation
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6 Contents
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8 Chapter 1. Introduction and preli
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10 Chapter 1. Introduction and prel
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28 Chapter 2. Submodular functions
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48 Chapter 3. Edge-connectivity aug
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70 Chapter 4. Connectivity augmenta
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Page 82 and 83: 82 Chapter 4. Connectivity augmenta
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Page 116 and 117: 116 Chapter 7. Combined augmentatio
Page 130 and 131: 130 Chapter 8. Concluding remarks w
Page 134 and 135: 134 Bibliography [38] S. Fujishige,
Page 136 and 137: 136 Bibliography [66] A. Schrijver,
Page 138 and 139: 138 Index in-degree of node, 19 ind
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Edge-connectivity of undirected and directed hypergraphs

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