Homomorphic Compactness of Infinite Graphs

Authors

Dr. Bruce L. Bauslaugh, Department of Mathematics and Statistics

Document Type

Presentation Abstract

Presentation Date

10-17-1997

Abstract

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)

Recommended Citation

Bauslaugh, Dr. Bruce L., "Homomorphic Compactness of Infinite Graphs" (1997). Colloquia of the Department of Mathematical Sciences. 8.
https://scholarworks.umt.edu/mathcolloquia/8