Felix Weilacher

activity

20182026

most citedBorel Edge Colorings for Finite Dimensional Groups

6 citations · 12 across the 16 of their papers we have counts for

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Showing math.LOShow all

17 papers · 1 filter

math.LO2026

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…

math.LO2026

Randomized Borel $(2 d + 1)$ -coloring of digraphs

Anton Bernshteyn, Edward Hou, Forte Shinko +1

Let $G$ be a Borel digraph with maximum out-degree $d \in N$ . We show that $G$ admits a random Borel $(2 d + 1)$ -coloring for which every edge is almost surely not monochroma…

math.LO2026

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…

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.LO2026

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…

math.LO2026

$G_{δ}$ Circle Squaring

Spencer Unger, Narmada Varadarajan, Felix Weilacher

We show that a circle and square of the same area in $R^{2}$ are equidecomposable by translations using $Δ_{2}^{0}$ pieces. That is, pieces which are simultaneously $F_{σ}$ …

math.LO2026

LCLs in the Borel Hierarchy

Felix Weilacher

A locally checkable labeling problem (LCL) on a group $Γ$ asks one to find a labeling of the Cayley graph of $Γ$ satisfying a fixed, finite set of "local" constraints. Typical exam…

math.LO2025

Separating complexity classes of LCL problems on grids

Katalin Berlow, Anton Bernshteyn, Clark Lyons +1

We study the complexity of locally checkable labeling (LCL) problems on $Z^{n}$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d.…

math.LO2024

Measurable Regular Subgraphs

Matt Bowen, Clinton T. Conley, Felix Weilacher

We show that every $d$ -regular bipartite Borel graph admits a Baire measurable $k$ -regular spanning subgraph if and only if $d$ is odd or $k$ is even. This gives the first example…

math.LO2023

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…

math.LO2022★ 2 cited

Computable vs Descriptive Combinatorics of Local Problems on Trees

Felix Weilacher

We study the position of the computable setting in the "common theory of locality" developed in arXiv:2106.02066 and arXiv:2204.09329 for local problems on $Δ$ -regular trees, $Δ\in…

math.LO2022★ 2 cited

Descriptive Combinatorics, Computable Combinatorics, and ASI Algorithms

Long Qian, Felix Weilacher

We introduce new types of local algorithms, which we call "ASI Algorithms", and use them to demonstrate a link between descriptive and computable combinatorics. This allows us to u…

math.LO2021

Definable Kőnig theorems

Matt Bowen, Felix Weilacher

Let $X$ be a Polish space with Borel probability measure $μ,$ and let $G$ be a Borel graph on $X$ with no odd cycles and maximum degree $Δ (G) .$ We show that the Baire measurable ed…

math.LO2021★ 6 cited

Borel Edge Colorings for Finite Dimensional Groups

Felix Weilacher

We study the potential of Borel asymptotic dimension, a tool introduced recently in arXiv:2009.06721, to help produce Borel edge colorings of Schreier graphs generated by Borel gro…

math.LO2021★ 2 cited

Borel Vizing's Theorem for 2-Ended Groups

Felix Weilacher

We show that Vizing's Theorem holds in the Borel context for graphs induced by actions of 2-ended groups, and ask whether it holds more generally for everywhere two ended Borel gra…

math.LO2020

Descriptive Chromatic Numbers of Locally Finite and Everywhere Two Ended Graphs

Felix Weilacher

We construct Borel graphs which settle several questions in descriptive graph combinatorics. These include "Can the Baire measurable chromatic number of a locally finite Borel grap…

math.LO2018

Marked Groups with Isomorphic Cayley Graphs but Different Borel Combinatorics

Felix Weilacher

We construct pairs of marked groups with isomorphic Cayley graphs but different Borel chromatic numbers for the free parts of their shift graphs. This answers a question of Kechris…

Hyperwellfoundedness and Eventual Domination

Randomized Borel (2d+1)-coloring of digraphs

Hyperfiniteness of bounded-to-one actions of commutative monoids

Measurable matchings in unbalanced graphs

Borel Homomorphisms from Forests to Kneser Graphs

Gδ​ Circle Squaring

LCLs in the Borel Hierarchy

Separating complexity classes of LCL problems on grids

Measurable Regular Subgraphs

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

Computable vs Descriptive Combinatorics of Local Problems on Trees

Descriptive Combinatorics, Computable Combinatorics, and ASI Algorithms

Definable Kőnig theorems

Borel Edge Colorings for Finite Dimensional Groups

Borel Vizing's Theorem for 2-Ended Groups

Descriptive Chromatic Numbers of Locally Finite and Everywhere Two Ended Graphs

Marked Groups with Isomorphic Cayley Graphs but Different Borel Combinatorics

Randomized Borel $(2 d + 1)$ -coloring of digraphs

$G_{δ}$ Circle Squaring