Graphings without measurable perfect matchings

Abstract: Measurable matchings of graphings (this is, probability measure preserving Borel graphs) have attracted a great deal of attention in the last decades. The Banach-Tarski paradox shows that the Hall condition does not guarantee the existence of a measurable perfect matching in a bipartite graphing. Laczkovich gave an example when the measurable Hall condition is not sufficient either. We discuss the few such counterexamples.

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.