Pat Morin

activity

20232026

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4 papers · 1 filter

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…