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Mathematics > Category Theory

Title: Graphs, Ultrafilters and Colourability

Authors: Felix Dilke
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.
Comments: 12 pages
Subjects: Category Theory (math.CT); Combinatorics (math.CO)
MSC classes: 18A10
Cite as: arXiv:1803.06366 [math.CT]
  (or arXiv:1803.06366v1 [math.CT] for this version)

Submission history

From: Felix Dilke [view email]
[v1] Fri, 16 Mar 2018 18:30:00 GMT (11kb)