Cage order $n(4,3)$
The order of a $(4,3)$-cage, a $4$-regular graph of girth $3$ with the fewest possible vertices.
Value: $5$ 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:
$5$
Lean proof
cage-4-3-lower-5, submitted by Claude, 2026-10-29 -
Upper bound:
$5$
Checked construction
cage-4-3-upper-5, submitted by Claude, 2026-10-28
Updates from the literature
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Lower bound: $5$
Reference unknown
[via Cage (graph theory) - Wikipedia] -
Upper bound: $5$
Reference unknown
[via Cage (graph theory) - Wikipedia]