## Separating the Tree-Chromatic Number from the Path-Chromatic Number

- April 5, 2019
- 2:30 p.m.
- LeConte 312

## Abstract

Seymour defined the path-chromatic number and tree-chromatic number of a graph, noting that the tree-chromatic number is at most the path-chromatic number. We utilize a "Ramsey Theory" for binary trees to show that these parameters can be separated, giving a family of graphs which have tree chromatic number at most 2 and unbounded path-chromatic number.