The Hamiltonicity threshold of the random graph G(n, p) (Komlós–Szemerédi)
A Lean 4 / Mathlib formalization of the sharp Hamiltonicity threshold of the binomial random graph: if ω(n) → ∞, then G(n, (log n + log log n + ω(n))/n) is Hamiltonian with probability tending to 1, and G(n, (log n + log log n − ω(n))/n) is Hamiltonian with probability tending to 0 (Komlós–Szemerédi 1983; Bollobás 1984). The edge probability is clipped to [0, 1] (min 1 above, max 0 below). The statements are given in the finite product model of the registered entry PALOMAR-2026-10-28-000021 (one independent Bernoulli(p) coin per pair of distinct vertices of Fin n) and, as corollaries, for…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-11-01-000032
curl -X POST /api/v1/records/palomar/PALOMAR-2026-11-01-000032/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-11-01-000032/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'