2021/06/03 by Kun, Gábor · 2 citations
#03E15 #05C21 #28D15 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2106.02013
We construct, for every d ≥ 3, a d-regular acyclic measurably bipartite graphing that admits no measurable perfect matching, resolving a problem of Kechris and Marks. A dense variant of our construction yields a coupling of two standard Borel probability measure spaces whose support contains no deterministic coupling, though the conditional probabilities of the coupling measure are atomless. This refutes a conjecture of Gurel-Gurevich and Peled.