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Continuous Edge Chromatic Numbers of Abelian Group Actions
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classification
math.COmath.LO
keywords
chromaticcontinuousedgemathbbgeneratingnumberabelianaction
abstract
We prove that for any generating set $S$ of $\mathbb {Z}^n$, the continuous edge chromatic number of the Schreier graph of the Bernoulli shift action $G=F(S,2^{\mathbb{Z}^n})$ is $\chi'_c(G)=\chi'(G)+1$. In particular, for the standard generating set, the continuous edge chromatic number of $F(2^{\mathbb {Z}^n})$ is $2n+1$.
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