Edge-connectivity of undirected and directed hypergraphs

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4 Contents 6 Hypergraph orientation 95 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.2 Orientation of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3 Orientation with supermodular requirements . . . . . . . . . . . . . . . . . 100 6.4 Directed network design problems with orientation constraints . . . . . . . 104 6.5 Local connectivity requirements . . . . . . . . . . . . . . . . . . . . . . . . 109 7 Combined augmentation and orientation 115 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 Augmentation to meet orientability requirements . . . . . . . . . . . . . . 116 7.3 (k, l)-partition-connectivity augmentation . . . . . . . . . . . . . . . . . . . 123 7.4 More general requirement functions . . . . . . . . . . . . . . . . . . . . . . 125 8 Concluding remarks 129
Acknowledgements I am greatly indebted to my supervisor, András Frank, who introduced me to this area of combinatorial optimization, and who helped me all the time by providing guidance and support, and by sharing his experience and unique understanding of the subject. His ideas and suggestions were essential for every new result of the thesis, and it was (and is) a real privilege for me to work with him. I am grateful to Zoltán Király and Márton Makai, with whom I worked on many of the results featured in the thesis. Apart from contributing their own results, they also helped a lot by suggesting changes to some of my less comprehensible proofs. For the same reason I am grateful to the unknown referees of our papers. I would like to thank every member of the Egerváry Research Group for the excellent atmosphere and highly motivating discussions. It is a rare joy to work in such a stimulating and enjoyable environment. Thanks are also due to Matthias Kriesell for his contribution, and to Katherina Langkau, Gábor Maróti, Satoru Iwata, and Alex Berg for fruitful discussions on some topics included in the thesis. Let me also express my thanks the staff of the Operations Research Depart- ment of Eötvös Loránd University, who provided invaluable help on many occasions. Finally, I am grateful to my family for giving every support I needed, and for tolerating my unusual working habits. 5
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84 Chapter 5. Partition-connectivit
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96 Chapter 6. Hypergraph orientatio
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130 Chapter 8. Concluding remarks w
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132 Bibliography [11] E. Cheng, Edg
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134 Bibliography [38] S. Fujishige,
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136 Bibliography [66] A. Schrijver,
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138 Index in-degree of node, 19 ind
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140 Index h(a) the head node of the
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142 Index
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Edge-connectivity of undirected and directed hypergraphs

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