6 citations · 12 across the 16 of their papers we have counts for
7 papers · 2 filters
Hyperwellfoundedness and Eventual Domination
Atticus Cull, Felix Weilacher
We prove that a Borel strict partial order is an increasing union of wellfounded Borel partial orders if and only if it admits an (injective) Borel homomorphism to the eventual dom…
Randomized Borel -coloring of digraphs
Anton Bernshteyn, Edward Hou, Forte Shinko +1
Let be a Borel digraph with maximum out-degree . We show that admits a random Borel -coloring for which every edge is almost surely not monochroma…
Hyperfiniteness of bounded-to-one actions of commutative monoids
Forte Shinko, Felix Weilacher, Jing Yu
A theorem of Dougherty--Jackson--Kechris states that any equivalence relation generated by a single Borel function is hypersmooth. A well-known open problem is whether this can be…
Measurable matchings in unbalanced graphs
Anton Bernshteyn, Matt Bowen, Felix Weilacher
Let be a locally finite multigraph that is bipartite and "unbalanced," meaning that it has a nontrivial bipartition with for all $x…
Borel Homomorphisms from Forests to Kneser Graphs
Felix Weilacher
We answer a recent question of Csóka and Vidnyánszky [arXiv:2407.10006] and give an alternate proof of one of their results. The subject of both is which finite graphs admit factor…
Circle Squaring
Spencer Unger, Narmada Varadarajan, Felix Weilacher
We show that a circle and square of the same area in are equidecomposable by translations using pieces. That is, pieces which are simultaneously …
LCLs in the Borel Hierarchy
Felix Weilacher
A locally checkable labeling problem (LCL) on a group asks one to find a labeling of the Cayley graph of satisfying a fixed, finite set of "local" constraints. Typical exam…