**UM Math Graduate Student Seminar**

Brittney Ellzey

* University of Miami *

**will present**

**Interval Graphs and Circular Arc Graphs**

Friday, September 9, 2016, 5:00pm

Ungar Building Room 402

**Abstract: **

Suppose we have a collection of n intervals on the real line. We can create a graph on n vertices by letting each interval correspond to a vertex and drawing an edge between two vertices if their corresponding intervals overlap. These graphs are called interval graphs. We will look at some examples of proper and unit interval graphs, as well as some different ways of characterizing them. We will also look at circular arc graphs, which are a generalization of interval graphs in which the intervals on the real line become arcs around a circle. If time permits, we will discuss some open problems involving the graphs mentioned and their chromatic symmetric/quasisymmetric functions.

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