Complexity and Algorithms for Graph and Hypergraph Sandwich Problems
β Scribed by Yair Caro; Raphael Yuster
- Publisher
- Springer Japan
- Year
- 1998
- Tongue
- English
- Weight
- 231 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
We consider extremal problems 'of Tur~ type' for r-uniform ordered hypergraphs, where multiple oriented edges are permitted up to multiplicity q. With any such '(r, q)-graph' G" we associate an r-linear form whose maximum over the standard (n -1)-simplex in R" is called the (graph-) density g(G ") o
Tuza, Z., Multipartite Turan problem for connected graphs and hypergraphs, Discrete Mathematics 112 (1993) 199-206. Giving a partial solution to a problem of Bialostocki and Dierker, we determine the maximum number of edges in a k-chromatic graph G with color classes of given cardinalities n,, , n,,
We show that for all large n, every n-uniform hypergraph with at most 0 7 n/ ln n Γ 2 n edges can be 2-colored. This makes progress on a problem of ErdΕs [Nordisk Mat. Tidskrift 11, 5-10 (1963)], improving the previous-best bound of n 1/3-o 1 Γ 2 n due to Beck [Discrete Math. 24, 127-137 (1978)]. We