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
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creator Campbell, Rutger
Distel, Marc
J Pascal Gollin
Harvey, Daniel J
Hendrey, Kevin
Hickingbotham, Robert
Mohar, Bojan
Wood, David R
description 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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title Graphs of Linear Growth have Bounded Treewidth
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