Kotzig's Perfect 1-Factorisation Conjecture, Asymptotically
Prior state unknown→proved
asymptotic form only; Kotzig's conjecture itself remains far from solved
SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review
combinatorics / Design theory
Kotzig's Perfect 1-Factorisation Conjecture, Asymptotically
Kotzig conjectured that for every even $n \ge 4$ the complete graph $K_n$ decomposes into $n-1$ perfect matchings such that every pair of them forms a Hamilton cycle. An asymptotic version holds: $K_n$ decomposes into $n-1$ perfect matchings of which $(1-o(1))n$ have the property that any pair forms a Hamilton cycle.
30Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts
Temporal state
Current frontier
No reconciled state yet.
Append-only history
Frontier timeline
Research memory
Claims and attempts
Scoped claims
Kotzig conjectured that for every even $n \ge 4$ the complete graph $K_n$ decomposes into $n-1$ perfect matchings such that every pair of them forms a Hamilton cycle. An asymptotic version holds: $K_n$ decomposes into $n-1$ perfect matchings of which $(1-o(1))n$ have the property that any pair forms a Hamilton cycle.
asymptotic form only; Kotzig's conjecture itself remains far from solved
Recorded attempts
Evidence graph
Connected research record
No public relationships recorded yet.