OAI/Combinatorics/Ramsey/CycleClique/Construction/WalkCycle.lean
2 declarations, 0 contain sorry, 0 declared as axioms
Convert the standard library's cycle walks into exact cycle witnesses.
- theorem
OAI.CycleClique.Construction.hasCycle_of_isCycleline 11 - theorem
OAI.CycleClique.Construction.hasCycle_of_path_closeline 28Source documentation
A simple path of at least two edges closes to an exact cycle when its endpoints are adjacent. This is the single-chain case of path closure.
theorem hasCycle_of_path_close {x y : V} {p : G.Walk x y} (hp : p.IsPath) (hlen : 2 ≤ p.length) (hclose : G.Adj y x) : HasCycle G (p.length + 1) := by …Mentions: OAI.CycleClique.Construction.HasCycle