# Graph Embeddings and Approximate Graph Coloring

### by François Labelle

under the supervision of Prof. Sue Whitesides
May 2000

### Abstract

We describe how to embed a graph into a small n-dimensional hypersphere such that the endpoints of any edge are placed exactly one unit of distance apart. As an application, we show how such an embedding can be used to find large independent sets in sparse 3-colorable graphs. By combining this algorithm with another which is specialized in dense graphs, we obtain a randomized, polynomial time algorithm that can color any 3-colorable graph using at most O(n^{1/4}log^{1/2}n) colors.
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page last updated: October 7, 2001