Theorems · Definition · combinatorics
SimpleGraph.IsBridge
{V : Type u} → SimpleGraph V → Sym2 V → PropAn edge of a graph is a bridge if without it, its incident vertices are not reachable from one another.
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coeproof · cited by 62,936
- SimpleGraphstatement and proof · cited by 3,072
- Sym2statement and proof · cited by 737
- SimpleGraph.Reachableproof · cited by 141
- SimpleGraph.deleteEdgesproof · cited by 64
- Sym2.liftproof · cited by 6
Cited by30
Results whose statement or proof uses this declaration.
- SimpleGraph.isBridge_iff_forall_cycle_notMemstatement · cited by 5
- SimpleGraph.isAcyclic_iff_forall_isBridgestatement and proof · cited by 4
- SimpleGraph.isBridge_iffstatement · cited by 3
- SimpleGraph.isAcyclic_iff_forall_adj_isBridgestatement and proof · cited by 2
- SimpleGraph.isBridge_iff_not_isEdgeReachable_twostatement and proof · cited by 2
- SimpleGraph.Connected.connected_delete_edge_of_not_isBridgestatement and proof · cited by 2
- SimpleGraph.isTree_of_minimal_connectedproof · cited by 1
- SimpleGraph.isAcyclic_starGraphproof · cited by 1
- SimpleGraph.isBridge_iff_forall_walk_mem_edgesstatement · cited by 1
- SimpleGraph.isBridge_sup_edgestatement · cited by 1
- SimpleGraph.IsBridge.antistatement and proof · cited by 1
- SimpleGraph.IsBridge.nontrivialstatement and proof · cited by 1