The complexity of colouring problems on dense graphs
Theoretical Computer Science
The maximum size of 3-uniform hypergraphs not containing a fano plane
Journal of Combinatorial Theory Series B
Coloring Bipartite Hypergraphs
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Dirac-Type Theorem for 3-Uniform Hypergraphs
Combinatorics, Probability and Computing
Perfect Matchings and K 43-Tilings in Hypergraphs of Large Codegree
Graphs and Combinatorics
Perfect matchings in large uniform hypergraphs with large minimum collective degree
Journal of Combinatorial Theory Series A
The Complexity of Almost Perfect Matchings in Uniform Hypergraphs with High Codegree
Combinatorial Algorithms
The Complexity of Perfect Matching Problems on Dense Hypergraphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Computational complexity of the hamiltonian cycle problem in dense hypergraphs
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Strong colorings of hypergraphs
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
H-colorings of dense hypergraphs
Information Processing Letters
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In this note we consider the problem of deciding whether a given r-uniform hypergraph H with minimum vertex degree at least c(|V(H)|-1 r-1), has a vertex 2-coloring and a strong vertex k-coloring. Motivated by an old result of Edwards for graphs, we summarize what can be deduced from his method about the complexity of these problems for hypergraphs. We obtain the first optimal dichotomy results for 2-colorings of 3- and 4-uniform hypergraphs according to the value of c. In addition, we determine the computational complexity of strong k-colorings of 3-uniform hypergraphs for some c, leaving a gap which vanishes as k→∞.