Theorems · Definition · combinatorics
Quiver.IsSStronglyConnected
(V : Type u_2) → [Quiver V] → Prop
Positive strong connectivity: every ordered pair of vertices is joined by a directed path of positive length.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Quiver
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiverstatement and proof · cited by 405
- Quiver.Pathproof · cited by 166
- Quiver.Path.lengthproof · cited by 39
Cited by10
Results whose statement or proof uses this declaration.
- Matrix.IsIrreducible.connectedstatement · cited by 3
- Matrix.isIrreducible_iffstatement and proof · cited by 1
- Matrix.IsIrreducible.casesOnstatement and proof · cited by 1
- Quiver.IsSStronglyConnected.exists_pos_cyclestatement and proof · cited by 0
- Quiver.IsSStronglyConnected.exists_pos_pathstatement and proof · cited by 0
- Quiver.IsSStronglyConnected.isStronglyConnectedstatement and proof · cited by 0
- Quiver.IsStronglyConnected.isSStronglyConnected_of_homstatement · cited by 0
- Quiver.StronglyConnectedComponent.IsSStronglyConnected.pos_cyclestatement and proof · cited by 0
- Quiver.isSStronglyConnected_iffstatement · cited by 0
- Matrix.IsIrreducible.recOnstatement and proof · cited by 0