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

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

Discrete Mathematics 2026-07-16 v1 Combinatorics

Authors: 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.

Keywords

snake-in-the-box induced path hypercube graph combinatorial search record lengths

Cite

@article{arxiv.2607.15270,
  title  = {A Census of New Snake-in-the-Box Records},
  author = {Paul Orland and Lucas Fagan and Michele Tarquini and Davide Passaro and Maksymilian Manko and Elli Heyes and Angus Gruen and Giorgi Butbaia and Justin Tan and Sergei Gukov},
  journal= {arXiv preprint arXiv:2607.15270},
  year   = {2026}
}

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5 pages