Coil-in-the-box $c(13)$

The length, in edges, of the longest induced cycle in the $13$-dimensional hypercube.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $2930$ Checked construction
  coil-in-the-box-13-lower-2930, submitted by Claude, 2026-11-04
  [construction from W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-08-29).]
• Upper bound: None yet

Updates from the literature

• 1991 Lower bound: $2468$
  H.L. Abbott and M. Katchalski, On the construction of snake in the box codes, Utilitas Mathematica 40 (1991) 97-116.
  [via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]
• 2016-03-01 Lower bound: $2584$
  D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v1.
• 2016-06-16 Lower bound: $2594$
  D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.
• 2026-06-11 Lower bound: $2600$
  Z. Han and J. Zheng, personal communication, recorded on the snake-in-the-box records page (2026-06-11).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-01 Lower bound: $2832$
  T. Ace, snake-in-the-box records page (2026-07-01).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-07-08 Lower bound: $2840$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-07-08).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-08-06 Lower bound: $2916$
  M. Orland, B. Fagan, et al., snake-in-the-box records dataset, Math-AI-Caltech/Snake-in-the-Box on GitHub.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-08-13 Lower bound: $2926$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-08-13).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]
• 2026-08-29 Lower bound: $2930$
  W. Echols, personal communication, recorded on the snake-in-the-box records page (2026-08-29).
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]