Generalized Connectivity of Graphs

Front Cover
Springer, Jun 30, 2016 - Mathematics - 143 pages

Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity.

This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.

 

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Contents

1 Introduction
1
2 Results for Some Graph Classes
15
3 Algorithm and Complexity
30
4 Sharp Bounds of the Generalized EdgeConnectivity
41
5 Graphs with Given Generalized Connectivity
58
6 NordhausGaddumType Results
67
7 Results for Graph Products
79
8 Maximum Generalized Local Connectivity
89
9 Generalized Connectivity for Random Graphs
113
Bibliography
134
Index
141
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