Theorems · Inductive type · combinatorics
SimpleGraph.Walk.IsCycle
{V : Type u} → {G : SimpleGraph V} → {u : V} → G.Walk u u → PropA cycle at u : V is a circuit at u whose only repeating vertex
is u (which appears exactly twice).
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 91 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement · cited by 3,072
- SimpleGraph.Walkstatement · cited by 915
Cited by97
Results whose statement or proof uses this declaration.
- SimpleGraph.IsAcyclicproof · cited by 67
- SimpleGraph.egirthproof · cited by 17
- SimpleGraph.Walk.IsCycle.isCircuitstatement and proof · cited by 14
- SimpleGraph.Walk.IsCycle.not_nilstatement and proof · cited by 14
- SimpleGraph.Walk.IsCycle.support_nodupstatement and proof · cited by 8
- SimpleGraph.Walk.IsHamiltonianCycle.toIsCyclestatement · cited by 8
- SimpleGraph.isBridge_iff_forall_cycle_notMemstatement and proof · cited by 5
- SimpleGraph.Walk.isCycle_map_iff_of_injectivestatement and proof · cited by 4
- SimpleGraph.egirth_eq_topproof · cited by 4
- SimpleGraph.egirth_le_lengthstatement and proof · cited by 4
- SimpleGraph.Walk.IsCycle.getVert_injOnstatement and proof · cited by 4
- SimpleGraph.Walk.IsCycle.isPath_tailstatement and proof · cited by 4