Coil-in-the-box $c(9)$

The length, in edges, of the longest induced cycle in the $9$-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: $192$ Checked construction
  coil-in-the-box-9-lower-192, submitted by Claude, 2026-11-04
  [construction from M. Orland, B. Fagan, et al., A census of new snake-in-the-box records, arXiv:2607.15270v1.]
• Upper bound: None yet

Updates from the literature

• 2005-09 Lower bound: $180$
  D.A. Casella and W.D. Potter, Using evolutionary techniques to hunt for snakes and coils, 2005 IEEE Congress on Evolutionary Computation, vol. 3, 2499-2505.
  [via Sequence A000937 in the OEIS]
• 2009-11 Lower bound: $186$
  E. Wynn, personal communication, recorded on the University of Georgia snake-in-the-box records page (2009).
  [via Snake-in-the-box records, Institute for Artificial Intelligence, University of Georgia (archived)]
• 2012-01-08 Lower bound: $188$
  E. Wynn, Constructing circuit codes by permuting initial sequences, arXiv:1201.1647.
• 2026-07-16 Lower bound: $192$
  M. Orland, B. Fagan, et al., A census of new snake-in-the-box records, arXiv:2607.15270v1.
  [via Snake-in-the-box records, Tom Ace, retrieved 2026-11-04]