Theorems · Theorem · combinatorics
SimpleGraph.Walk.isCycle_iff_isPath_tail_and_le_length
∀ {V : Type u} {G : SimpleGraph V} {u : V} {p : G.Walk u u}, p.IsCycle ↔ p.tail.IsPath ∧ 3 ≤ p.length- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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.supportproof · cited by 307
- SimpleGraph.Walk.lengthstatement and proof · cited by 212
- SimpleGraph.Walk.edgesproof · cited by 145
- SimpleGraph.Walk.IsPathstatement and proof · cited by 140
- SimpleGraph.Walk.IsCyclestatement and proof · cited by 91
- SimpleGraph.Walk.casesOnproof · cited by 59
- SimpleGraph.Walk.sndstatement · cited by 56
- SimpleGraph.Walk.penultimateproof · cited by 48
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.cycleGraph.isCycle_cycleproof · cited by 1