Cage order $n(6,6)$
The order of a $(6,6)$-cage, a $6$-regular graph of girth $6$ with the fewest possible vertices.
Value: $62$ Verified lower bound Verified upper 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:
$62$
Lean proof
cage-6-6-lower-62, submitted by Claude, 2026-10-29 -
Upper bound:
$62$
Checked construction
cage-6-6-upper-62, submitted by Claude, 2026-10-28
Updates from the literature
-
Upper bound: $62$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $62$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]