Pat Morin

activity

20232026

collaborators

11 papers

math.CO2026

Far-apart Erdős--Pósa property of long cycles

Maria Chudnovsky, Vida Dujmović, Gwenaël Joret +4

We prove that there exist functions $f : N^{2} \to N$ and $g : N \to N$ such that for all positive integers $k$ , $d$ , and $ℓ \geq 3$ , every graph $G$ either c…

math.CO2026

3-Colouring Graphs Excluding a Fixed Minor

Vida Dujmović, Hussein Houdrouge, Pat Morin

We show that, for every fixed graph $H$ , every $n$ -vertex graph $G$ that excludes $H$ as a minor is $3$ -colourable with clustering $O_{H} (n^{4/9})$ . That is, there exists a function…

cs.DM2026

Adjacency labelling for proper minor-closed graph classes

Vida Dujmović, Cyril Gavoille, Gwenaël Joret +3

We show that every proper minor-closed class of graphs admits a $(1 + o (1)) lo g_{2} n$ -bit adjacency labelling scheme. Equivalently, for every proper minor-closed class $G$ a…

math.CO2026

2-dimensional unit vector flows

Hussein Houdrouge, Bobby Miraftab, Pat Morin

We study $2$ -dimensional unit vector flows on graphs, that is, nowhere-zero flows that assign to each oriented edge a unit vector in $R^{3}$ . We give a new geometric charac…

math.CO2025

3-Colouring Planar Graphs

Vida Dujmović, Pat Morin, Sergey Norin +1

We show that every $n$ -vertex planar graph is 3-colourable with monochromatic components of size $O (n^{4/9})$ . The best previous bound was $O (n^{1/2})$ due to Linial, Matoušek, She…

math.CO2024

Erdős--Pósa property of cycles that are far apart

Vida Dujmović, Gwenaël Joret, Piotr Micek +1

We prove that there exist functions $f, g : N \to N$ such that for all nonnegative integers $k$ and $d$ , for every graph $G$ , either $G$ contains $k$ cycles such that…

math.CO2024

On $k$ -planar Graphs without Short Cycles

Michael A. Bekos, Prosenjit Bose, Aaron Büngener +6

We study the impact of forbidding short cycles to the edge density of $k$ -planar graphs; a $k$ -planar graph is one that can be drawn in the plane with at most $k$ crossings per edg…

math.CO2024

Planar graphs in blowups of fans

Marc Distel, Vida Dujmović, Gwenaël Joret +3

We show that every $n$ -vertex planar graph is contained in the graph obtained from a fan by blowing up each vertex by a complete graph of order $O (n lo g^{2} n)$ . Equivalently,…

math.CO2024

Vertex Ranking of Degenerate Graphs

John Iacono, Piotr Micek, Pat Morin +1

An $ℓ$ -vertex-ranking of a graph $G$ is a colouring of the vertices of $G$ with integer colours so that in any connected subgraph $H$ of $G$ with diameter at most $ℓ$ , there…

math.CO2024

Grid Minors and Products

Vida Dujmović, Pat Morin, David R. Wood +1

Motivated by recent developments regarding the product structure of planar graphs, we study relationships between treewidth, grid minors, and graph products. We show that the Carte…

cs.DM2023

Local certification of geometric graph classes

Oscar Defrain, Louis Esperet, Aurélie Lagoutte +2

The goal of local certification is to locally convince the vertices of a graph $G$ that $G$ satisfies a given property. A prover assigns short certificates to the vertices of the g…

Far-apart Erdős--Pósa property of long cycles

3-Colouring Graphs Excluding a Fixed Minor

Adjacency labelling for proper minor-closed graph classes

2-dimensional unit vector flows

3-Colouring Planar Graphs

Erdős--Pósa property of cycles that are far apart

On k-planar Graphs without Short Cycles

Planar graphs in blowups of fans

Vertex Ranking of Degenerate Graphs

Grid Minors and Products

Local certification of geometric graph classes

On $k$ -planar Graphs without Short Cycles