- Current Students
- Future Students
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.
Place: 315 Armstrong Hall
All are welcome.