Improving the performance guarantee for approximate graph coloring
Journal of the ACM (JACM)
Graph properties and hypergraph colourings
Discrete Mathematics
A still better performance guarantee for approximate graph coloring
Information Processing Letters
New approximation algorithms for graph coloring
Journal of the ACM (JACM)
The complexity of generalized graph colorings
Discrete Applied Mathematics
An Õ(n3/14)-coloring algorithm for 3-colorable graphs
Information Processing Letters
Coloring Bipartite Hypergraphs
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximate Hypergraph Coloring
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Coloring 2-colorable hypergraphs with a sublinear number of colors
Nordic Journal of Computing
Zero Knowledge and the Chromatic Number
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximate graph coloring by semidefinite programming
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Strong colorings of hypergraphs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
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We consider an algorithmic problem of coloring r-uniform hypergraphs. The problem of finding the exact value of the chromatic number of a hypergraph is known to be NP-hard, so we discuss approximate solutions to it. Using a simple construction and known results on hardness of graph coloring, we show that for any r ≥ 3 it is impossible to approximate in polynomial time the chromatic number of r-uniform hypergraphs on n vertices within a factor n1-Ɛ for any Ɛ 0, unless NP ⊆ ZPP. On the positive side, we present an approximation algorithm for coloring r-uniform hypergraphs on n vertices, whose performance ratio is O(n(log log n)2=(log n)2). We also describe an algorithm for coloring 3-uniform 2-colorable hypergraphs on n vertices in Õ (n9/41) colors, thus improving previous results of Chen and Frieze and of Kelsen, Mahajan and Ramesh.