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Graduate Seminar

Jing Zhang
CMU
Title: The refined chromatic compactness theorem for certain graphs

Abstract: De Bruijn and Erdos proved that the chromatic number of a graph of any size is less or equal to k iff every finite subgraph has chromatic number less or equal to k. Here k is a finite number. There are two natural questions: 1) Do we have to look at all finite subgraphs? or just finite subgraphs of certain size? 2) Can k be an infinite cardinal? We will address these two questions. The answer to 1) is yes, granted some restrictions on the graph. The answer to 2) is yes, granted restrictions on the graphs and more axioms other than ZFC.

Date: Tuesday, February 6, 2018
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Son Van