Theorems · Theorem · combinatorics
SimpleGraph.Walk.isTrail_def
∀ {V : Type u} {G : SimpleGraph V} {u v : V} (p : G.Walk u v), p.IsTrail ↔ p.edges.Nodup- Defined in
- Mathlib.Combinatorics.SimpleGraph.Paths
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Walkstatement and proof · cited by 915
- Sym2statement · cited by 737
- SimpleGraph.Walk.edgesstatement and proof · cited by 145
- SimpleGraph.Walk.IsTrailstatement and proof · cited by 62
- SimpleGraph.Walk.IsTrail.casesOnproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.isTrail_map_iff_of_injectiveproof · cited by 5
- SimpleGraph.Walk.IsEulerian.isTrailproof · cited by 4
- SimpleGraph.Walk.IsTrail.of_mapproof · cited by 2
- SimpleGraph.Walk.isTrail_rotateproof · cited by 2
- SimpleGraph.reachable_deleteEdges_iff_exists_cycle.auxproof · cited by 1
- SimpleGraph.IsAcyclic.isPath_iff_isTrailproof · cited by 0