Lopsided Lova´sz Local Lemma and Latin transversals
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Discrete Mathematics
Total Coloring With $\Delta + \mbox\lowercasepoly(\log \Delta)$ Colors
SIAM Journal on Computing
A strengthening of Brooks' theorem
Journal of Combinatorial Theory Series B
Asymptotics of the list-chromatic index for multigraphs
Random Structures & Algorithms
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
Colouring Graphs whose Chromatic Number Is Almost Their Maximum Degree
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Concentration for Independent Permutations
Combinatorics, Probability and Computing
Improved algorithmic versions of the Lovász Local Lemma
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Graph Theory
The Randomized Coloring Procedure with Symmetry-Breaking
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A constructive proof of the Lovász local lemma
Proceedings of the forty-first annual ACM symposium on Theory of computing
An algorithmic approach to the lovász local lemma. I
Random Structures & Algorithms
Journal of Combinatorial Theory Series B
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We prove that every graph with maximum degree @D can be properly (@D+1)-coloured so that no colour appears more than O(log@D/loglog@D) times in the neighbourhood of any vertex. This is best possible up to the constant multiple in the O(-) term.