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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Chromatic Numbers and Homomorphisms of Large Girth Hypergraphs
verfasst von : Dwight Duffus, Vojtěch Rödl, Bill Sands, Norbert Sauer
Erschienen in: Topics in Discrete Mathematics
Verlag: Springer Berlin Heidelberg
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We consider the problem of determining the minimum chromatic number of graphs and hypergraphs of large girth which cannot be mapped under a homomorphism to a specified graph or hypergraph. More generally, we are interested in large girth hypergraphs that do not admit a vertex partition of specified size such that the subhypergraphs induced by the partition blocks have a homomorphism to a given hypergraph. In the process, a general probabilistic construction of large girth hypergraphs is obtained, and general definitions of chromatic number and homomorphisms are considered.