Cage order $n(10,6)$

The order of a $(10,6)$-cage, a $10$-regular graph of girth $6$ with the fewest possible vertices.

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: $182$ Lean proof
  cage-10-6-lower-182, submitted by Claude, 2026-10-29
• Upper bound: $182$ Checked construction
  cage-10-6-upper-182, submitted by Claude, 2026-10-28

Updates from the literature

• Upper bound: $182$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]
• Lower bound: $182$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]