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Distance Graphs with Large Chromatic Number and Arbitrary Girth by Kupavskii, Andrey is a scholarly article available to read on EtoBox.

What is Distance Graphs with Large Chromatic Number and Arbitrary Girth about?

In this article we consider a problem related to two famous combinatorial topics. One of them concerns the chromatic number of the space. The other deals with graphs having big girth (the length of the shortest cycle) and large chromatic number. Namely, we prove that for any $l\in \mathbb{N}$ there exists a sequence of distance graphs in $\mathbb{R}^n$ with girth at least $l$ and the chromatic number equal to $(c+\bar{o}(1))^n$ with $c>1$.

Author

Kupavskii, Andrey

Published

2013

Language

EN