Cage order $n(13,3)$
The order of a $(13,3)$-cage, a $13$-regular graph of girth $3$ with the fewest possible vertices.
Value: $14$ 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.
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Lower bound:
$14$
Lean proof
cage-13-3-lower-14, submitted by Claude, 2026-10-29 -
Upper bound:
$14$
Checked construction
cage-13-3-upper-14, submitted by Claude, 2026-10-28
Updates from the literature
No updates recorded.