# Homomorphic Compactness of Infinite Graphs

## 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.

## 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

## Additional Details

Friday, October 17, 1997

4:10 p.m. in MA 109

Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)