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arXiv · 2607.15270

A Census of New Snake-in-the-Box Records

Paul Orland·Lucas Fagan·Michele Tarquini·Davide Passaro·Maksymilian Manko·Elli Heyes·Angus Gruen·Giorgi Butbaia·Justin Tan·Sergei Gukov
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Abstract

The snake-in-the-box problem, introduced by Kautz in 1958, asks for the longest induced (chordless) path, called a snake, in the hypercube graph $Q_n$. The maximum length $a(n)$ is known in each dimension $n \leq 8$. We give snakes that are longer than the previous best-known in every dimension from $9$ to $13$, improving the lower bound on $a(n)$. All record-length paths are provided in a computer-verifiable dataset.

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Paul Orland, Lucas Fagan, Michele Tarquini, Davide Passaro, Maksymilian Manko, Elli Heyes, Angus Gruen, Giorgi Butbaia, Justin Tan, Sergei Gukov. 2026-07-20. A Census of New Snake-in-the-Box Records. https://arxiv.org/abs/2607.15270

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