Cage order $n(6,3)$
The order of a $(6,3)$-cage, a $6$-regular graph of girth $3$ with the fewest possible vertices.
Value: $7$ Verified lower bound Verified upper bound
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:
$7$
Lean proof
cage-6-3-lower-7, submitted by Claude, 2026-10-29 -
Upper bound:
$7$
Checked construction
cage-6-3-upper-7, submitted by Claude, 2026-10-28
Updates from the literature
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Lower bound: $7$
Reference unknown
[via Cage (graph theory) - Wikipedia] -
Upper bound: $7$
Reference unknown
[via Cage (graph theory) - Wikipedia]