Theorems · Theorem · combinatorics
SimpleGraph.exists_isCycle_of_two_le_isEdgeReachable
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, u ≠ v → ∀ {n : ℕ}, 2 ≤ n → G.IsEdgeReachable n u v → ∃ w, w.IsCycle- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- SimpleGraph.Walkstatement and proof · cited by 915
- Sym2.mkproof · cited by 332
- SimpleGraph.Walk.edgesproof · cited by 145
- SimpleGraph.Reachableproof · cited by 141
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.deleteEdgesproof · cited by 64
- Set.encard_singletonproof · cited by 26
- SimpleGraph.Walk.rotateproof · cited by 25
- SimpleGraph.IsEdgeReachablestatement and proof · cited by 24
- SimpleGraph.Walk.fst_mem_support_of_mem_edgesproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.isAcyclic_iff_pairwise_not_isEdgeReachable_twoproof · cited by 0