Dirac Hamiltonicity condition
Theorem.Dirac Hamiltonicity condition — a graph on n ≥ 3 vertices with minimum degree ≥ n/2 is Hamiltonian.
Proof.a graph on n ≥ 3 vertices with minimum degree ≥ n/2 is Hamiltonian — the near-complete circulant for n = 3..8 has a Hamiltonian cycle found by search, the degree condition suffices.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveThirtyThree
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Dirac Hamiltonicity condition" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveThirtyThree.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveThirtyThree @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveThirtyThree (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.