Row pathwidth of complete binary trees

Abstract

We show that if a complete binary tree of height $h$ is isomorphic to a subgraph of the strong product of a graph $H$ and a path, then $\mathrm{pw}(H)$ is $\Omega(h)$. This solves a problem posed by Bose, Dujmovi\'c, Javarsineh, Morin, and Wood (2022). The proof was found by OpenAI's GPT-5.6 Sol Pro.