On the chromatic number and independence number of hypergraph products
✍ Scribed by Dhruv Mubayi; Vojtěch Rödl
- Book ID
- 108167407
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 106 KB
- Volume
- 97
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For a pair of integers 1 F ␥r, the ␥-chromatic number of an r-uniform Ž . hypergraph H s V, E is the minimal k, for which there exists a partition of V into subsets < < T, . . . , T such that e l T F ␥ for every e g E. In this paper we determine the asymptotic 1 k i Ž . behavior of the ␥-chromatic n
We present a hypergraph coloring algorithm and analyze its performance in spaces of random hypergraphs. In these spaces the number of colors used by our algorithm is almost surely within a small constant factor (less than 2) of the weak chromatic number of the hypergraph. This also establishes new u
Burr recently proved [3] that for positive integers m , , m 2 , . . , , m, and any graph G we have x(G) 5 &, if and only if G can be expressed as the edge disjoint union of subgraphs F, satisfying x(F,) 5 m,. This theorem is generalized to hypergraphs. By suitable interpretations the generalization