Some intersection theorems for ordered sets and graphs
Journal of Combinatorial Theory Series A
Asymptotic behavior of the chromatic index for hypergraphs
Journal of Combinatorial Theory Series A
Induced matchings in bipartite graphs
Discrete Mathematics - In memory of Tory Parsons
Size and independence in triangle-free graphs with maximum degree three
Journal of Graph Theory
A parallel algorithmic version of the Local Lemma
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Coloring nearly-disjoint hypergraphs with n+o(n) colors
Journal of Combinatorial Theory Series A
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
A still better performance guarantee for approximate graph coloring
Information Processing Letters
Journal of Combinatorial Theory Series B
Lower bounds on the competitive ration for mobile user tracking and distributed job scheduling
Theoretical Computer Science - Special issue on dynamic and on-line algorithms
Relating path coverings to vertex labellings with a condition at distance two
Discrete Mathematics
Modern probabilistic methods in combinatorics
Surveys in combinatorics, 1995
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Asymptotically good list-colorings
Journal of Combinatorial Theory Series A
Asymptotics of the chromatic index for multigraphs
Journal of Combinatorial Theory Series B
A bound on the strong chromatic index of a graph
Journal of Combinatorial Theory Series B
An entropy proof of Bergman's theorem
Journal of Combinatorial Theory Series A
Subgraphs with a large cochromatic number
Journal of Graph Theory
Total colorings of planar graphs with large maximum degree
Journal of Graph Theory
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Color-critical graphs on a fixed surface
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
List edge and list total colourings of multigraphs
Journal of Combinatorial Theory Series B
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Counting 1-factors in regular bipartite graphs
Journal of Combinatorial Theory Series B
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Total Coloring With $\Delta + \mbox\lowercasepoly(\log \Delta)$ Colors
SIAM Journal on Computing
The Complexity of Near-Optimal Graph Coloring
Journal of the ACM (JACM)
Coloring graphs with sparse neighborhoods
Journal of Combinatorial Theory Series B
Random Structures & Algorithms
Asymptotics of the list-chromatic index for multigraphs
Random Structures & Algorithms
Proceedings of the ninth international conference on on Random structures and algorithms
Circular chromatic number: a survey
Discrete Mathematics
A new proof of the independence ratio of triangle-free cubic graphs
Discrete Mathematics
Colouring graphs when the number of colours is nearly the maximum degree
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Planar graphs of maximum degree seven are Class I
Journal of Combinatorial Theory Series B
Encyclopedia of Mathematics and Its Applications: The Theory of Information and Coding: A Mathematical Framework for Communication
Concrete Math
Boolean functions whose Fourier transform is concentrated on the first two levels
Advances in Applied Mathematics
Colouring Graphs whose Chromatic Number Is Almost Their Maximum Degree
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Nonrepetitive colorings of graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
A Theorem about the Channel Assignment Problem
SIAM Journal on Discrete Mathematics
Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The Chromatic Number of Graph Powers
Combinatorics, Probability and Computing
Concentration for Independent Permutations
Combinatorics, Probability and Computing
An Entropy Approach to the Hard-Core Model on Bipartite Graphs
Combinatorics, Probability and Computing
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Multilevel Distance Labelings for Paths and Cycles
SIAM Journal on Discrete Mathematics
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
The Channel Assignment Problem with Variable Weights
SIAM Journal on Discrete Mathematics
An upper bound for the chromatic number of line graphs
European Journal of Combinatorics
Labeling planar graphs with a condition at distance two
European Journal of Combinatorics
Fourier analysis and large independent sets in powers of complete graphs
Journal of Combinatorial Theory Series B
Labelings of Graphs with Fixed and Variable Edge-Weights
SIAM Journal on Discrete Mathematics
Improved algorithmic versions of the Lovász Local Lemma
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
On total 9-coloring planar graphs of maximum degree seven
Journal of Graph Theory
Acyclic edge colorings of graphs
Journal of Graph Theory
Coloring the square of a planar graph
Journal of Graph Theory
Circular choosability of graphs
Journal of Graph Theory
The acyclic edge chromatic number of a random d-regular graph is d + 1
Journal of Graph Theory
Journal of Graph Theory
Total chromatic number of planar graphs with maximum degree ten
Journal of Graph Theory
On two questions about circular choosability
Journal of Graph Theory
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
SIAM Journal on Discrete Mathematics
Bounding χ in terms of ω and Δ for quasi-line graphs
Journal of Graph Theory
Total-Coloring of Plane Graphs with Maximum Degree Nine
SIAM Journal on Discrete Mathematics
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
On Moore graphs with diameters 2 and 3
IBM Journal of Research and Development
An algorithmic approach to the lovász local lemma. I
Random Structures & Algorithms
Random Structures & Algorithms
Combinatorial optimization in system configuration design
Automation and Remote Control
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The application of the probabilistic method to graph colouring has been yielding interesting results for more than 40 years. Several probabilistic tools are presented in this survey, ranging from the basic to the more advanced. For each of them, an application to a graph colouring problem is presented in detail. In this way, not only is the general idea of the method exposed, but also are the concrete details arising with its application. Further, this allows us to introduce some important variants of the usual graph colouring notion (with some related open questions), and at the same time to illustrate the variety of the probabilistic technics. The survey tries to be self-contained.