Asymptotically good list-colorings
Journal of Combinatorial Theory Series A
A bound on the strong chromatic index of a graph
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
A strengthening of Brooks' theorem
Journal of Combinatorial Theory Series B
Colouring Graphs whose Chromatic Number Is Almost Their Maximum Degree
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Uniquely Colourable Graphs and the Hardness of Colouring Graphs of Large Girth
Combinatorics, Probability and Computing
Journal of Graph Theory
Journal of Combinatorial Theory Series B
Path coupling using stopping times and counting independent sets and colorings in hypergraphs
Random Structures & Algorithms
Dichotomy for bounded degree H-colouring
Discrete Applied Mathematics
Asymptotically optimal frugal colouring
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Asymptotically optimal frugal colouring
Journal of Combinatorial Theory Series B
The complexity of changing colourings with bounded maximum degree
Information Processing Letters
Survey: Randomly colouring graphs (a combinatorial view)
Computer Science Review
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We consider for graphs of maximum degree &Dgr;, the problem of determining whether &khgr;G) &Dgr;-k for various values of k. We obtain sharp theorems characterizing when the barrier to &Dgr;-k colourability must be a local condition, i.e. a small subgraph, and when it can be global. We also show that for large fixed &Dgr;, this problem is either NP-complete or can be solved in linear time, and we determine precisely which values of k correspond to each case prove that Hitting Set with sets of size B is hard to approximate to within a factor $B^{1/19}$. The problem can be approximated to within a factor B [19], and it is the Vertex Cover problem for B=2. The relationship between hardness of approximation and set size seems to have not been explored before.