Graphs of Linear Growth have Bounded Treewidth

Graphs of Linear Growth have Bounded Treewidth

A graph class \(\mathcal{G}\) has linear growth if, for each graph \(G \in \mathcal{G}\) and every positive integer \(r\), every subgraph of \(G\) with radius at most \(r\) contains \(O(r)\) vertices. In this paper, we show that every graph class with linear growth has bounded treewidth.

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Veröffentlicht in:arXiv.org 2022-10
Hauptverfasser: Campbell, Rutger, Distel, Marc, J Pascal Gollin, Harvey, Daniel J, Hendrey, Kevin, Hickingbotham, Robert, Mohar, Bojan, Wood, David R
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graph theory
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Zusammenfassung:A graph class \(\mathcal{G}\) has linear growth if, for each graph \(G \in \mathcal{G}\) and every positive integer \(r\), every subgraph of \(G\) with radius at most \(r\) contains \(O(r)\) vertices. In this paper, we show that every graph class with linear growth has bounded treewidth.
ISSN:2331-8422