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Graph Colouring and the Probabilistic Method

BuchGebunden
326 Seiten
Englisch
Springererschienen am20.11.2001
Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method.mehr
Verfügbare Formate
BuchGebunden
EUR149,79
E-BookPDF1 - PDF WatermarkE-Book
EUR139,09

Produkt

KlappentextOver the past decade, many major advances have been made in the field of graph colouring via the probabilistic method.
Zusammenfassung
The book covers a topic of central interest to discrete mathematics.- The authors are two of the very best on this topic.

Includes supplementary material: sn.pub/extras
Details
ISBN/GTIN978-3-540-42139-9
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2001
Erscheinungsdatum20.11.2001
ReiheAlgorithms and Combinatorics
Seiten326 Seiten
SpracheEnglisch
Gewicht642 g
IllustrationenXIV, 326 p.
Artikel-Nr.11785162

Inhalt/Kritik

Inhaltsverzeichnis
1. Colouring Preliminaries.- 2. Probabilistic Preliminaries.- 3. The First Moment Method.- 4. The Lovász Local Lemma.- 5. The Chernoff Bound.- 6. Hadwiger´s Conjecture.- 7. A First Glimpse of Total Colouring.- 8. The Strong Chromatic Number.- 9. Total Colouring Revisited.- 10. Talagrand´s Inequality and Colouring Sparse Graphs.- 11. Azuma´s Inequality and a Strengthening of Brooks´ Theorem.- 12. Graphs with Girth at Least Five.- 13. Triangle-Free Graphs.- 14. The List Colouring Conjecture.- 15. The Structural Decomposition.- 16. ?, ? and ?.- 17. Near Optimal Total Colouring I: Sparse Graphs.- 18. Near Optimal Total Colouring II: General Graphs.- 19. Generalizations of the Local Lemma.- 20. A Closer Look at Talagrand´s Inequality.- 21. Finding Fractional Colourings and Large Stable Sets.- 22. Hard-Core Distributions on Matchings.- 23. The Asymptotics of Edge Colouring Multigraphs.- 24. The Method of Conditional Expectations.- 25. Algorithmic Aspects of the Local Lemma.- References.mehr
Kritik
From the reviews of the first edition:



"The presented book contains many ... chapters, each of which presents a proof technique and apply that for a certain graph coloring problem. ... The book ends with a vast bibliography. We think that this well-written monograph will serve as a main reference on the subject for years to come." (János Barát, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

"The book is a pleasure to read; there is a clear, successful attempt to present the intuition behind the proofs, making even the difficult, recent proofs of important results accessible to potential readers. ... The book is highly recommended to researchers and graduate students in graph theory, combinatorics, and theoretical computer science who wish to have this ability." (Noga Alon, SIAM Review, Vol. 45 (2), 2003)

"The probabilistic method in graph theory was initiated by Paul Erdös in 1947 ... . This book is an introduction to this powerful method. ... The book is well-written and brings the researcher to the frontiers of an exciting field." (M.R. Murty, Short Book Reviews, Vol. 23 (1), April, 2003)

"This monograph provides an accessible and unified treatment of major advances made in graph colouring via the probabilistic method. ... Many exercises and excellent remarks are presented and discussed. Also very useful is the list of up-to-date references for current research. This monograph will be useful both to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability." (Jozef Fiamcik, Zentralblatt MATH, Vol. 987 (12), 2002)mehr