Open Research Index

Dirac's theorem: k vertices of a k-connected graph lie on a common cycle

Juan Pablo Traverso Gianini

Palomar Registrypalomar/PALOMAR-2026-10-18-000011Oct 18, 2026math.COscore 0

A Lean 4 / Mathlib formalization of Dirac's 1960 theorem: in a k-connected finite simple graph with k ≥ 2 (more than k vertices, and connected after deleting any set of fewer than k vertices), any set of at most k vertices lies on a common cycle. In particular, in a 2-connected finite graph any two vertices lie on a common cycle. Cycles are Mathlib's `SimpleGraph.Walk.IsCycle`. Mathlib does not have this theorem.

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