Edward Hou

activity

20222026

collaborators

4 papers

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.LO2025

Borel Polychromatic Number of Grids

Katalin Berlow, Edward Hou

We study Borel polychromatic colorings of grid graphs arising from free Borel actions of $Z^{d}$ . A polychromatic coloring is one in which every unit $d$ -dimensional cube se…

math.LO2022

A note on measure-theoretic domatic partitions

Edward Hou

We show that if $(X, μ)$ is a standard probability space, then every $μ$ -preserving $ℵ_{0}$ -regular Borel graph on $X$ admits a $μ$ -measurable vertex $ℵ_{0}$ -coloring in which…

math.LO2022

Measurable domatic partitions

Edward Hou

Let $Γ$ be a compact Polish group of finite topological dimension. For a countably infinite subset $S \subseteq Γ$ , a domatic $ℵ_{0}$ -partition (for its Schreier graph on $Γ$ ) is…

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

Borel Polychromatic Number of Grids

A note on measure-theoretic domatic partitions

Measurable domatic partitions

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