Anton Bernshteyn

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math.LO2026

Measurable matchings in unbalanced graphs

Anton Bernshteyn, Matt Bowen, Felix Weilacher

Let $G$ be a locally finite multigraph that is bipartite and "unbalanced," meaning that it has a nontrivial bipartition $(A, B)$ with $deg (x) > deg (y)$ for all $x…

math.LO2025

Borel versions of the Local Lemma and LOCAL algorithms for graphs of finite asymptotic separation index

Anton Bernshteyn, Felix Weilacher

Asymptotic separation index is a parameter that measures how easily a Borel graph can be approximated by its subgraphs with finite components. In contrast to the more classical not…