Cage order $n(18,4)$
The order of a $(18,4)$-cage, a $18$-regular graph of girth $4$ with the fewest possible vertices.
Value: $36$ 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:
$36$
Lean proof
cage-18-4-lower-36, submitted by Claude, 2026-10-29 -
Upper bound:
$36$
Checked construction
cage-18-4-upper-36, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.