P. Micek

activity

20242026

collaborators

5 papers

math.CO2026

Note on the treewidth of graphs excluding a disjoint union of cycles as a minor

Gwenaël Joret, Piotr Micek

For a planar graph $H$ , let $f (H)$ denote the minimum integer such that all graphs excluding $H$ as a minor have treewidth at most $f (H)$ . We show that if $H$ is a disjoint union o…

math.CO2026

A coarse Gallai theorem

Marc Distel, Ugo Giocanti, Jędrzej Hodor +2

We prove that there exist functions $f$ and $g$ such that for all positive integers $k$ and $d$ , for every graph $G$ and every subset $A$ of the vertices of $G$ , either $G$ contain…

math.CO2025

Planarity and dimension I

Heather Smith Blake, Jędrzej Hodor, Piotr Micek +2

The dimension of a partially ordered set $P$ (poset for short) is the least positive integer $d$ such that $P$ is isomorphic to a subposet of $R^{d}$ with the natural produc…

math.CO2025

Shallow brambles

Nicolas Bousquet, Wouter Cames van Batenburg, Louis Esperet +2

A graph class $C$ has polynomial expansion if there is a polynomial function $f$ such that for every graph $G \in C$ , each of the depth- $r$ minors of $G$ has ave…

math.CO2024

Centered colorings in minor-closed graph classes

Jędrzej Hodor, Hoang La, Piotr Micek +1

A vertex coloring $φ$ of a graph $G$ is $p$ -centered if for every connected subgraph $H$ of $G$ , either $φ$ uses more than $p$ colors on $H$ , or there is a color that appears exact…