The Hardness of 3-Uniform Hypergraph Coloring
✍ Scribed by Irit Dinur*; Oded Regev†; Clifford Smyth‡
- Publisher
- Springer-Verlag
- Year
- 2005
- Tongue
- English
- Weight
- 263 KB
- Volume
- 25
- Category
- Article
- ISSN
- 0209-9683
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📜 SIMILAR VOLUMES
We discuss approximation algorithms for the coloring problem and the maximum independent set problem in 3-uniform hypergraphs. An algorithm for coloring ˜1r5 Ž . ## 3-uniform 2-colorable hypergraphs in O n colors is presented, improving previously known results. Also, for every fixed ␥ ) 1r2, we
## Abstract Here improving on our earlier results, we prove that there exists an __n__~0~ such that for __n__⩾__n__~0~ in every 2‐coloring of the edges of __K__ there is a monochromatic Hamiltonian 3‐tight Berge cycle. This proves the __c__=2, __t__=3, __r__=4 special case of a conjecture from (P.
A conjecture of Bollobás and Thomason asserts that, for r ≥ 1, every r -uniform hypergraph with m edges can be partitioned into r classes such that every class meets at least rm/(2r -1) edges. Bollobás, Reed and Thomason [3] proved that there is a partition in which every edge meets at least (1 -1/e