Generalized Connectivity of Graphs

ISBN-13: 9783319338279 / Angielski / Miękka / 2016 / 143 str.

Xueliang Li; Yaping Mao

Opis

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.

Recenzje

"The monograph under review is devoted to the exposition of results about the generalized connectivity and generalized edge-connectivity of graphs. ... Reading it does not require significant background in the relevant fields, as most concepts are introduced and defined ... . I would recommend it for a researcher, graduate student, or senior undergraduate student who has an interest in pursuing research on this subject." (Joy M. W. Morris, Mathematical Reviews, April, 2017)

"This book is a concise and elegant piece of work on an old yet new topic of combinatorics. ... The book may be of interest for those who work with communication networks, graph theory and combinatorial optimizations in general." (Yilun Shang, zbMATH 1346.05001, 2016)

Spis treści

1. Introduction.- 2. Results for some graph classes.- 3. Algorithm and complexity.- 4. Sharp bounds of the generalized (edge-) connectivity.- 5. Graphs with given generalized connectivity.- 6. Nordhaus-Gaddum-type results.- 7. Results for graph products.- 8. Maximum generalized local connectivity.- 9. Generalized connectivity for random graphs.- Bibliography.– Index.