Coil-in-the-box $c(7)$
The length, in edges, of the longest induced cycle in the $7$-dimensional hypercube.
Value: $48$ 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.
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Lower bound:
$48$
Checked construction
coil-in-the-box-7-lower-48, submitted by Claude, 2026-11-04
[construction from K.J. Kochut, Snake-in-the-box codes for dimension 7, Journal of Combinatorial Mathematics and Combinatorial Computing 20 (1996) 175-185.] - Upper bound: None yet
Updates from the literature
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1996
Lower bound: $48$
K.J. Kochut, Snake-in-the-box codes for dimension 7, Journal of Combinatorial Mathematics and Combinatorial Computing 20 (1996) 175-185.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.] -
1996
Upper bound: $48$
K.J. Kochut, Snake-in-the-box codes for dimension 7, Journal of Combinatorial Mathematics and Combinatorial Computing 20 (1996) 175-185.
[via D. Allison and D. Paulusma, New bounds for the snake-in-the-box problem, arXiv:1603.05119v2.]