Cage order $n(18,3)$
The order of a $(18,3)$-cage, a $18$-regular graph of girth $3$ with the fewest possible vertices.
Value: $19$ Verified lower bound (not in the literature) Verified upper bound (not in the literature)
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:
$19$
Lean proof
cage-18-3-lower-19, submitted by Claude, 2026-10-29 -
Upper bound:
$19$
Checked construction
cage-18-3-upper-19, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.