Molloy / Reed Graph Colouring and the Probabilistic Method
Erscheinungsjahr 2013
ISBN: 978-3-642-04016-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 326 Seiten, Web PDF
Reihe: Mathematics and Statistics (R0)
ISBN: 978-3-642-04016-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
The topics covered include: Kahn's proofs that the Goldberg-Seymour and List Colouring Conjectures hold asymptotically; a proof that for some absolute constant C, every graph of maximum degree Delta has a Delta+C total colouring; Johansson's proof that a triangle free graph has a O(Delta over log Delta) colouring; algorithmic variants of the Local Lemma which permit the efficient construction of many optimal and near-optimal colourings.
This begins with a gentle introduction to the probabilistic method and will be useful to researchers and graduate students in graph theory, discrete mathematics, theoretical computer science and probability.
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.
