Author

G. Joret

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Open access Aug 2026

Hardness of Linear Variants of the Balanced Minimum Evolution Problem

A cubic tree is a tree with leaves in which every internal vertex has degree exactly 3. Any such tree can be encoded by a Path‐Length Matrix (PLM), that is, an integer matrix whose th entry gives the number of edges in the unique path between leaves and in . The convex hull of all PLMs associated with cubic tre...

D. Catanzaro, G. Joret, Brieuc Pierre et al. · Networks · 0 citations

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 Sep 2026

Induced Forest Minor Theorem for Graphs Without an Induced Star

Motivated by recent work on tree independence number, we study the path independence number of a graph $G$: the minimum integer $k$ such that there is a path decomposition of $G$ where each bag induces a graph with independence number at most $k$. We show that every graph excluding both an induced forest minor and an i...

Robert Hickingbotham, G. Joret · 1 citation