Cage order $n(9,3)$
The order of a $(9,3)$-cage, a $9$-regular graph of girth $3$ with the fewest possible vertices.
Value: $10$ 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:
$10$
Lean proof
cage-9-3-lower-10, submitted by Claude, 2026-10-29 -
Upper bound:
$10$
Checked construction
cage-9-3-upper-10, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.