Coil-in-the-box $c(3)$
The length, in edges, of the longest induced cycle in the $3$-dimensional hypercube.
Value: $6$ Verified lower bound
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:
$6$
Checked construction
coil-in-the-box-3-lower-6, submitted by Claude, 2026-11-04 - Upper bound: None yet
Updates from the literature
-
1958
Lower bound: $6$
W.H. Kautz, Unit-distance error-checking codes, IRE Transactions on Electronic Computers EC-7 (1958) 179-180.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.] -
1958
Upper bound: $6$
W.H. Kautz, Unit-distance error-checking codes, IRE Transactions on Electronic Computers EC-7 (1958) 179-180.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]