Homomorphic Compactness of Infinite Graphs

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The University of CalgaryIn 1951 de Bruijn and Erdös proved that an infinite graph is n-colourable if and only if each of its finite subgraphs is n- colourable. This is often referred to as 'compactness of n-colouring'. Using the fact that n-colouring is essentially identical to finding a graph homomorphism to a complete graph on n vertices, we say that a graph G is homomorphically compact if each infinite graph H admits a homomorphism to G exactly when all of its finite subgraphs admit such a homomorphism.

We will show that (really) infinite compact graphs exist and explore various other problems related to them.

Additional Details

Friday, October 17, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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