MARC Record from harvard_bibliographic_metadata

LEADER: 03524nam a22005175a 4500
001 013841974-4
005 20131206202635.0
008 130626s2002 gw | s ||0| 0|eng d
020 $a9783642040160
020 $a9783642040160
020 $a9783642040153
024 7 $a10.1007/978-3-642-04016-0$2doi
035 $a(Springer)9783642040160
040 $aSpringer
050 4 $aQA164-167.2
072 7 $aPBV$2bicssc
072 7 $aMAT036000$2bisacsh
082 04 $a511.6$223
100 1 $aMolloy, Michael,$eauthor.
245 10 $aGraph Colouring and the Probabilistic Method /$cby Michael Molloy, Bruce Reed.
264 1 $aBerlin, Heidelberg :$bSpringer Berlin Heidelberg :$bImprint: Springer,$c2002.
300 $aXIV, 326 p.$bonline resource.
336 $atext$btxt$2rdacontent
337 $acomputer$bc$2rdamedia
338 $aonline resource$bcr$2rdacarrier
347 $atext file$bPDF$2rda
490 1 $aAlgorithms and Combinatorics,$x0937-5511 ;$v23
505 0 $aColouring Preliminaries -- Probabilistic Preliminaries -- The First Moment Method -- The Lovasz Local Lemma -- The Chernoff Bound -- Hadwiger's Conjecture -- A First Glimpse of Total Colouring -- The Strong Chromatic Number -- Total Colouring Revisited -- Talagrand's Inequality and Colouring Sparse Graphs -- Azuma's Inequality and a Strengthening of Brooks'Theorem -- Graphs with Girth at Least Five -- Triangle-Free Graphs -- The List Colouring Conjecture -- A Structural Decomposition -- Omega,Delta, and Chi -- Near Optimal Total Colouring I: Sparse Graphs -- Near Optimal Total Colouring II: General Graphs -- Generalizations of the Local Lemma -- A Closer Look at Talagrand's Inequality -- Finding Fractional Colourings and Large Stable Sets -- Hardcore Distribution on Matchings -- The Asymptotics of Edge Colouring Multigraphs -- The Method of Conditional Expectation -- Algorithmic Aspects of the Local Lemma.
520 $aOver 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.
650 20 $aCombinatorial analysis.
650 10 $aMathematics.
650 0 $aDistribution (Probability theory)
650 0 $aCombinatorial analysis.
650 0 $aMathematics.
650 0 $aInformation theory.
650 0 $aComputer software.
650 0 $aComputer science.
650 24 $aProbability Theory and Stochastic Processes.
650 24 $aTheory of Computation.
650 24 $aMath Applications in Computer Science.
650 24 $aAlgorithm Analysis and Problem Complexity.
700 1 $aReed, Bruce,$eauthor.
776 08 $iPrinted edition:$z9783642040153
830 0 $aAlgorithms and Combinatorics ;$v23.
988 $a20131119
906 $0VEN