Edward Hou

collaborators

3 papers

math.LO2025

A note on measure-theoretic domatic partitions

Edward Hou

We show that if $(X, I^¼)$ is a standard probability space, then every $I^¼$ -preserving $ℵ_{0}$ -regular Borel graph on $X$ admits a $I^¼$ -measurable vertex $ℵ_{0}$ -coloring in wh…

math.LO2025

Measurable domatic partitions

Edward Hou

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

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…