Author

W. Cames van Batenburg

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Preprint Sep 2026

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

We show that every planar graph with no $t \times t$ grid minor has treewidth at most $4t +4$. This improves on the previously best known bound of $\frac{9}{2}t - \frac{11}{2}$, due to Gu and Tamaki (2012), and is within a factor $2$ of optimal. A key step in the proof is showing the following result, which might be of...

Wouter Cames van Batenburg, Quentin Claus, G. Joret et al. · 0 citations

Preprint Aug 2026

Counterexamples to the Albertson-Berman conjecture: minimum order, connectivity and an improved ratio bound

In 1979, Albertson and Berman conjectured that every planar graph $G$ contains an induced forest of order at least $|V(G)|/2$. This long-standing conjecture was recently disproved by several explicit counterexamples, which naturally led to several extremal and structural questions that we answer. We combine mathematica...

Wouter Cames van Batenburg, J. Goedgebeur, Jorik Jooken · 0 citations

Preprint Aug 2026

Asymptotically attaining the Moore bound

For positive integers $d$ and $k$, let $n_k(d)$ be the maximum order of a graph of maximum degree at most $d$ and diameter at most $k$. We prove that $$ \lim_{d\to\infty}\frac{n_k(d)}{d^k}=1$$ for every fixed $k$, thereby resolving the asymptotic degree-diameter problem for fixed diameter and proving a conjecture of Bo...

Wouter Cames van Batenburg, Samuel Korsky · 0 citations