Theorems · Theorem · combinatorics
SimpleGraph.cycleGraph_isContained_iff
∀ {V : Type u_1} {G : SimpleGraph V} {n : ℕ},
2 < n → ((SimpleGraph.cycleGraph n).IsContained G ↔ ∃ v p, p.IsCycle ∧ p.length = n)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- SimpleGraphstatement and proof · cited by 3,072
- zero_addproof · cited by 2,366
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Walk.supportproof · cited by 307
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.IsPathproof · cited by 140
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.IsContainedstatement and proof · cited by 68
- SimpleGraph.Walk.mapproof · cited by 66
- SimpleGraph.Adj.symmproof · cited by 66
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isAcyclic_iff_free_cycleGraphproof · cited by 1