IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

## Combinatorial Nullstellensatz

• Sept. 26, 2014
• 2:30 p.m.
• LeConte 312

## Abstract

In 1999, Noga Alon introduced the method of Combinatorial Nullstellensatz, one of several examples of how techniques from Algebraic Geometry are being used to make advances in discrete mathematics. In this talk, we will demonstrate the utility of C.N. with a few examples. In particular, we will look at application to antimagic labeling of graphs. A graph with $m$ edges is antimagic provided there is an edge-labeling with distinct integers from $\{1, 2, \ldots, m\}$ such that, when each vertex is assigned the sum of the labels of its incident edges, no two vertex sums are equal. In 1990, Hartsfield and Ringel conjectured that every simple connected graph aside from $K _ 2$ is antimagic. One group making progress toward this conjecture using Combinatorial Nullstellensatz was formed at the Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics this summer.