From Coloring Planar Graphs to Choosability in Vector Spaces

Document Type

Presentation Abstract

Presentation Date

9-7-2001

Abstract

Tutte discovered an interesting connection between coloring planar graphs and nowhere-zero flows. For planar dual graphs G and G*, he showed that k-colorings of G dualize no nowhere-zero k-flows of G*. Based on this duality, Tutte made three fascinating conjectures concerning nowhere-zero flows. All three of these conjectures are still open.

After exploring this duality and discussing some known properties of nowhere-zero flows, we move on to a more general perspective:

choosability in vector spaces. In this realm we discuss what is known to be true and what is conjectured to be true. In particular, we give two choosability theorems about matrices over fields of characteristic two which generalize Jaeger's 4-flow and 8-flow theorems, and we suggest a new conjecture about matrices over fields of odd characteristic which would imply Tutte's 5-flow conjecture.

Additional Details

This talk is part of The Big Sky Conference, sponsored by the National Science Foundation and the Department of Mathematical Sciences.

Friday, 7 September 2001
4:10 p.m. in James E Todd Building CE 203-204
Reception at 3:30 p.m. CE 204

This document is currently not available here.

Share

COinS