Treewidth 2 in the Planar Graph Product Structure Theorem

• DOI: 10.46298/dmtcs.14785
• Publication Date: 2025-03-17T09:35:06Z
• Authors: Marc Distel; Kevin Hendrey; Nikolai Karol; David R. Wood; Jung Hon Yip

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 $H \boxtimes T \boxtimes K_c$.Comment: arXiv admin note: text overlap with arXiv:2410.20333