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
Oriented hypergraphs, stability numbers and chromatic numbers
✍ Scribed by Heinrich Müller
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 232 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
Oriented hypergraphs are defined, so that it is possible to genc&ze popositions characterizing the chromatic number and the stability number of a graph by means of crientations i!tnd elementary paths, to the strong and weak chromatic number and the strong and we& stability number of a hypergraph.
📜 SIMILAR VOLUMES
We determine the strong total chromatic number of the complete h-uniform hypergraph Kh, and the complete h-partite hypergraph K,\* ............ .
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
The oriented chromatic number χ o ( G) of an oriented graph G = (V, A) is the minimum number of vertices in an oriented graph H for which there exists a homomorphism of G to H. The oriented chromatic number χ o (G) of an undirected graph G is the maximum of the oriented chromatic numbers of all the
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We wrote many papers on these subjects, some in collaboration with Galvin, Rado, Shelah and Szemer6di, and posed many problems some of which turned out to be undecidable. In this survey we state some old and new solved and unsolved problems. Nous avons 6crit beaucoup d'articles, certains en collabo