Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.Preconnected

{V : Type u} → SimpleGraph V → Prop

A graph is preconnected if every pair of vertices is reachable from one another.

Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
49 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.Connected.preconnected · cited by 28Connected.preconnectedSimpleGraph.connected_iff · cited by 6SimpleGraph.connected_iffSimpleGraph.connected_iff_exists_forall_reachable · cited by 6SimpleGraph.connected_iff…SimpleGraph.Subgraph.Preconnected.coe · cited by 5Preconnected.coeSimpleGraph.Subgraph.connected_iff · cited by 5Subgraph.connected_iffSimpleGraph.Subgraph.preconnected_iff · cited by 5Subgraph.preconnected_iffSimpleGraph.Preconnected.map · cited by 2Preconnected.mapSimpleGraph.Preconnected.mono · cited by 2Preconnected.monoSimpleGraph.Preconnected.of_subsingleton · cited by 2Preconnected.of_subsingle…SimpleGraph.Preconnected.support_eq_univ · cited by 2Preconnected.support_eq_u…SimpleGraph.pathGraph_preconnected · cited by 2SimpleGraph.pathGraph_pre…SimpleGraph.preconnected_bot_iff_subsingleton · cited by 2SimpleGraph.preconnected_…SimpleGraph.preconnected_induce_iff · cited by 2SimpleGraph.preconnected_…SimpleGraph.Connected.casesOn · cited by 2Connected.casesOnSimpleGraph.Preconnected.degree_pos_of_nontrivial · cited by 2Preconnected.degree_pos_o…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.Reachable · cited by 141SimpleGraph.ReachableSimpleGraph.PreconnectedCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by53

Results whose statement or proof uses this declaration.