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arXiv · 2411.00343

Treewidth 2 in the Planar Graph Product Structure Theorem

Marc Distel·Kevin Hendrey·Nikolai Karol·David R. Wood·Jung Hon Yip
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Abstract

We prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any $c \in \mathbb{N}$, there is a planar graph $G$ such that for any tree $T$ and graph $H$ with $\text{tw}(H) \leqslant 2$, $G$ is not contained in $H \boxtimes T \boxtimes K_c$.

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Marc Distel, Kevin Hendrey, Nikolai Karol, David R. Wood, Jung Hon Yip. 2025-03-13. Treewidth 2 in the Planar Graph Product Structure Theorem. https://doi.org/10.46298/dmtcs.14785

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