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arXiv · 1803.06366

Graphs, Ultrafilters and Colourability

Felix Dilke
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Abstract

Let $\beta$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $\beta$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $\beta G$ on the set $\beta V$ of ultrafilters on V . In what follows, we interrelate the properties of G and $\beta G$. Perhaps the most striking result is that G can be finitely coloured iff $\beta G$ has no loops.

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Felix Dilke. 2018-03-16. Graphs, Ultrafilters and Colourability. https://arxiv.org/abs/1803.06366

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