Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraph
∀ {V : Type u} {G : SimpleGraph V} (H : G.Subgraph),
H.Preconnected ↔ ∀ {u v : V}, u ∈ H.verts → v ∈ H.verts → ∃ p, p.toSubgraph ≤ H- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Walkstatement and proof · cited by 915
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.Subgraph.coeproof · cited by 89
- SimpleGraph.Walk.mapproof · cited by 66
- SimpleGraph.Walk.toSubgraphstatement and proof · cited by 49
- SimpleGraph.Subgraph.homproof · cited by 18
- SimpleGraph.Reachable.mapproof · cited by 14
- SimpleGraph.Subgraph.Preconnectedstatement and proof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.connected_iff_forall_exists_walk_subgraphproof · cited by 0