# Close Enough! How to (Probably) Calculate the Chromatic Number

## Document Type

Presentation Abstract

## Presentation Date

5-2-2022

## Abstract

How many colours does it take to paint every vertex of a graph if edges can't connect vertices of the same colour? This is a difficult problem to answer, so instead, let's figure out how to make the smartest guess. Rather than writing an algorithm that determines this so-called chromatic number, what can we say about its distribution when a graph is chosen at random? This problem boasts over seventy years of clever tricks, not only from probability and graph theory but also linear algebra, complex analysis, and even statistical physics. In this talk, we'll look at some of these breakthroughs as well as some recent progress I've made with coauthors Karen Gunderson and Xavier Pérez-Giménez.

## Recommended Citation

Nir, JD, "Close Enough! How to (Probably) Calculate the Chromatic Number" (2022). *Colloquia of the Department of Mathematical Sciences*. 628.

https://scholarworks.umt.edu/mathcolloquia/628

## Additional Details

May 2, 2022 at 3:00 p.m. Math 103 & Zoom