Quentin Claus

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math.CO2026

An improved bound on the treewidth of planar graphs excluding a grid minor

Wouter Cames van Batenburg, Quentin Claus, Gwenaël Joret +3

We show that every planar graph with no $t \times t$ grid minor has treewidth at most $4 t + 4$ . This improves on the previously best known bound of $\frac{9}{2} t - \frac{11}{2}$ , du…

math.CO2026

Erdős-Pósa property of rooted tree minors

Quentin Claus, Gwenaël Joret, Clément Rambaud +1

Fiorini, Joret, and Wood (2013) showed that tree minors satisfy the so-called Erdős-Pósa property with a linear bound: For every tree $T$ there exists a constant $c \geq 1$ such th…

math.CO2026

Blow-up structure of graphs excluding a tree or an apex-tree as a minor

Quentin Claus, Gwenaël Joret, Clément Rambaud

We prove blow-up structure theorems for graphs excluding a tree or an apex-tree as a minor. First, we show that for every $t$ -vertex tree $T$ with $t \geq 3$ and radius $h$ , and eve…

math.CO2026

Excluding an apex-forest or a fan as quickly as possible

Quentin Claus, Jędrzej Hodor, Gwenaël Joret +1

We show that every graph $G$ excluding an apex-forest $H$ as a minor has layered pathwidth at most $∣ V (H) ∣ - 2$ , and that every graph $G$ excluding an apex-linear forest (such as a f…