##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Mary Radcliffe

#### UCSD

## On the Hadwiger-Nelson Problem

##### Abstract:

Define a graph G by taking the vertices as $\mathbb{R}^2$ and the edges to be any pair of vertices that are distance 1 apart. The Hadwiger-Nelson Problem asks the chromatic number of this graph, written $\chi(\mathbb{R}^2)$. It is known that either $4\leq \chi(\mathbb{R}^2)\leq 7$ or $5\leq \chi(\mathbb{R}^2)\leq 7$. We explore some approaches to solving this problem, encountering along the way the Axiom of Choice (or lack thereof) and other infinite oddities.

### April 5, 2012

### 12:30 PM

### AP&M B402

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