# David Offner

Polychromatic Colorings on Hypercubes, Complete Graphs, and Integers

Abstract: Given a set S, and a set T of subsets of S, a coloring of the elements of S is called T -polychromatic if every set in T contains an element of every color. Let polyT (S) be the largest n for which there is a T -polychromatic coloring of S with n colors. This talk introduces theorems and open problems on the value of polyT (S) in three settings:

• S is the set of edges of a hypercube, and T is the set of all subgraphs isomorphic to

a given graph H.

• S is the set of edges of a complete graph, and T is the set of all regular spanning

subgraphs of a given degree.

• S is the set of integers, and T is the set of translates of a given finite set.

Date: 4/26/2017

Time: 3:30PM-4:30PM

Place: 315 Armstrong Hall

All are welcome.