Chromatic Numbers and Homomorphisms of Large Girth Hypergraphs.

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. [ABSTRACT FROM AUTHOR]