E-Book, Englisch, Band 23, 326 Seiten, eBook
Reihe: Algorithms and Combinatorics
Molloy / Reed Graph Colouring and the Probabilistic Method
2002
ISBN: 978-3-642-04016-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 23, 326 Seiten, eBook
Reihe: Algorithms and Combinatorics
ISBN: 978-3-642-04016-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Over the past decade, many major advances have been made in the field of graph coloring via the probabilistic method. This monograph, by two of the best on the topic, provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
