Cage order $n(4,6)$
The order of a $(4,6)$-cage, a $4$-regular graph of girth $6$ with the fewest possible vertices.
Value: $26$ 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.
-
Lower bound:
$26$
Lean proof
cage-4-6-lower-26, submitted by Claude, 2026-10-29 -
Upper bound:
$26$
Checked construction
cage-4-6-upper-26, submitted by Claude, 2026-10-28
Updates from the literature
-
Upper bound: $26$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26] -
Lower bound: $26$
Reference unknown
[via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]