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arXiv · 2505.19926

Bounding Width on Graph Classes of Constant Diameter

Konrad K. Dabrowski·Tala Eagling-Vose·Noleen Köhler·Sebastian Ordyniak·Daniël Paulusma
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Abstract

We determine if the width of a graph class ${\cal G}$ changes from unbounded to bounded if we consider only those graphs from ${\cal G}$ whose diameter is bounded. As parameters we consider treedepth, pathwidth, treewidth and clique-width, and as graph classes we consider classes defined by forbidding some specific graph $F$ as a minor, induced subgraph or subgraph, respectively. Our main focus is on treedepth for $F$-subgraph-free graphs of diameter at most~$d$ for some fixed integer $d$. We give classifications of boundedness of treedepth for $d\in \{4,5,\ldots\}$ and partial classifications for $d=2$ and $d=3$.

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Konrad K. Dabrowski, Tala Eagling-Vose, Noleen Köhler, Sebastian Ordyniak, Daniël Paulusma. 2025-05-26. Bounding Width on Graph Classes of Constant Diameter. https://arxiv.org/abs/2505.19926

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