Theorems · Theorem · combinatorics
SimpleGraph.Subgraph.connected_iff
∀ {V : Type u} {G : SimpleGraph V} {H : G.Subgraph}, H.Connected ↔ H.Preconnected ∧ H.verts.Nonempty- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemproof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Set.Nonemptystatement and proof · cited by 2,627
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.Subgraph.coeproof · cited by 89
- SimpleGraph.Preconnectedproof · cited by 49
- SimpleGraph.Subgraph.Connectedstatement · cited by 24
- Set.nonempty_coe_sortproof · cited by 23
- SimpleGraph.Subgraph.Preconnectedstatement and proof · cited by 14
- SimpleGraph.connected_iffproof · cited by 6
- SimpleGraph.Subgraph.preconnected_iffproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.Connected.nonemptyproof · cited by 3
- SimpleGraph.Subgraph.Connected.preconnectedproof · cited by 3
- SimpleGraph.Subgraph.Connected.mapproof · cited by 1
- SimpleGraph.Subgraph.connected_iff_forall_exists_walk_subgraphproof · cited by 0
- SimpleGraph.Connected.toSubgraphproof · cited by 0