Cage order $n(19,4)$
The order of a $(19,4)$-cage, a $19$-regular graph of girth $4$ with the fewest possible vertices.
Value: $38$ 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:
$38$
Lean proof
cage-19-4-lower-38, submitted by Claude, 2026-10-29 -
Upper bound:
$38$
Checked construction
cage-19-4-upper-38, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.