Open Research Index

Ore's and Dirac's Theorems on Hamiltonian Cycles

Noah Cohen

Palomar Registrypalomar/PALOMAR-2026-09-03-000001Sep 3, 2026math.COscore 0

A complete machine-checked Lean 4 formalization of Ore's theorem (1960) and Dirac's theorem (1952) on the existence of Hamiltonian cycles in simple graphs. Proves Ore's degree-sum condition via maximal path cycle-closure and connectivity arguments, and derives Dirac's minimum-degree theorem as a corollary. To the maintainers' knowledge, the theorem was not found in an exact declaration name, docstring, and type signature search of the pinned Mathlib revision (Mathlib v4.34.0-rc1).

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