6 papers
Continuous graph homomorphisms of higher dimensional abelian group actions
Ruijun Wang
For every fixed integer , we prove that the finite graphs receiving a continuous homomorphism from the standard Schreier graph form a -complete…
Finite Borel asymptotic dimension of bounded-to-one commutative monoid actions
Ruijun Wang
We prove that every bounded-to-one action of a finitely generated commutative monoid has finite asymptotic dimension, without a freeness assumption. If the group completion has tor…
Borel graphs generated by finitely many bounded-to-1 commuting Borel functions and hyperfinite equivalence relations
Ruijun Wang
We show that a Borel graph generated by finitely many bounded-to-1 commuting functions is hyperfinite. This recovers a theorem in the forthcoming paper by Naryshkin, Shinko, Weilac…
The continuous oriented chromatic number of directed Schreier graphs of -shift actions
Ruijun Wang
Let be the directed Schreier graph on the free part of the Bernoulli shift , with arcs in the two coordinate…
Borel Kernels in Borel Directed Graphs
Ruijun Wang
We prove that there is a Borel quasi-kernel in any locally countable Borel directed graph with finite Borel chromatic number. We prove that the Borel chromatic number of a Borel di…
Continuous Edge Chromatic Numbers of Abelian Group Actions
Su Gao, Ruijun Wang, Tianhao Wang
We prove that for any generating set of , the continuous edge chromatic number of the Schreier graph of the Bernoulli shift action is $…