“Distinguishing two notions of unique colorability for digraphs”

Document Type

Presentation Abstract

Presentation Date

4-10-2019

Abstract

The study of homomorphisms is ubiquitous in mathematics. In graph theory, homomorphisms naturally generalize the notion of coloring. Many other important problems regarding the chromatic number, the clique number, the odd girth number, etc., can also be restated in terms of homomorphisms. In this talk we focus on a special directed graph homomorphism known as the “acyclic homomorphism” and study two ways of generalizing the notion of unique colorability using it. One natural way to do this is to define it in terms of partitions induced by acyclic homomorphisms, while a second way—mostly used in the literature— is done by automorphisms of digraphs. We show that these two approaches are not equivalent and study conditions under which they coincide. This mirrors analogous work by Bonato (2007) in the realm of (undirected) graphs.

Additional Details

Link to the presenter's dissertation.

Wednesday, April 10, 2019 3:00 pm in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

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