# Spring 2018¶

We meet 4:00–5:30 in Evans room 1011.

## Monday, February 26¶

Vector Representations of Graphs and the Maximum Cut Problem (slides | video)

In this talk, I will look at a classical problem from graph theory of finding a large cut in a graph. We’ll start with a 1967 result of Erdős that showed that picking a random partition of the graph finds a cut that is at least half the largest possible cut. We’ll then describe a result due to Goemans and myself from 1995 that shows that by representing the graph as a set of vectors, one per vertex, and optimizing the set, one can find a cut of size at least .878 the largest possible. If time permits, we’ll see an additional application of this vector representation to either clustering or coloring.