Theorems · Theorem · combinatorics
SimpleGraph.isBridge_iff_not_isEdgeReachable_two
∀ {V : Type u_1} {G : SimpleGraph V} {u v : V}, G.Adj u v → (G.IsBridge s(u, v) ↔ ¬G.IsEdgeReachable 2 u v)An edge is a bridge iff its endpoints are not 2-edge-reachable.
The forward direction of this is true without assuming u and v are adjacent.
See IsBridge.not_isEdgeReachable_two.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- eq_or_neproof · cited by 1,117
- Sym2proof · cited by 737
- Sym2.mkstatement and proof · cited by 332
- Set.encardproof · cited by 327
- lt_of_le_of_neproof · cited by 230
- SimpleGraph.Reachableproof · cited by 141
- SimpleGraph.deleteEdgesproof · cited by 64
- SimpleGraph.IsBridgestatement and proof · cited by 30
- SimpleGraph.IsEdgeReachablestatement and proof · cited by 24
Cited by2
Results whose statement or proof uses this declaration.
- SimpleGraph.isBridge_iff_adj_and_not_isEdgeConnected_twoproof · cited by 0
- SimpleGraph.isAcyclic_iff_pairwise_not_isEdgeReachable_twoproof · cited by 0