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Graph Colouring and the Probabilistic Method
Michael Molloy
Bruce Reed
出版
Springer Science & Business Media
, 2013-06-29
主題
Mathematics / Probability & Statistics / General
Mathematics / Combinatorics
Computers / Computer Science
Computers / Data Science / General
Computers / Programming / Algorithms
Mathematics / Probability & Statistics / Stochastic Processes
Mathematics / Discrete Mathematics
ISBN
3642040160
9783642040160
URL
http://books.google.com.hk/books?id=gU3xCAAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
Over the past decade, many major advances have been made in the field of graph colouring via the probabilistic method. This monograph provides an accessible and unified treatment of these results, using tools such as the Lovasz Local Lemma and Talagrand's concentration inequality.
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.