Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.ConnectedComponent

{V : Type u} → SimpleGraph V → Type u

The quotient of V by the SimpleGraph.Reachable relation gives the connected components of a graph.

Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
86 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.ConnectedComponent.supp · cited by 42ConnectedComponent.suppSimpleGraph.connectedComponentMk · cited by 40SimpleGraph.connectedComp…SimpleGraph.ComponentCompl · cited by 29SimpleGraph.ComponentComplSimpleGraph.ConnectedComponent.toSimpleGraph · cited by 14ConnectedComponent.toSimp…SimpleGraph.ConnectedComponent.map · cited by 11ConnectedComponent.mapSimpleGraph.ConnectedComponent.Represents · cited by 10ConnectedComponent.Repres…SimpleGraph.oddComponents · cited by 10SimpleGraph.oddComponentsSimpleGraph.ConnectedComponent.sound · cited by 9ConnectedComponent.soundSimpleGraph.ConnectedComponent.ind · cited by 7ConnectedComponent.indSimpleGraph.ConnectedComponent.connected_toSimpleGraph · cited by 6ConnectedComponent.connec…SimpleGraph.ConnectedComponent.toSubgraph · cited by 5ConnectedComponent.toSubg…SimpleGraph.Iso.connectedComponentEquiv · cited by 5Iso.connectedComponentEqu…SimpleGraph.ConnectedComponent.mem_supp_iff · cited by 4ConnectedComponent.mem_su…SimpleGraph.ConnectedComponent.ind₂ · cited by 3ConnectedComponent.ind₂SimpleGraph.ConnectedComponent.toSimpleGraph_hom · cited by 3ConnectedComponent.toSimp…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.Reachable · cited by 141SimpleGraph.ReachableSimpleGraph.ConnectedComponentCITED BYCITES

Cites2

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

Cited by104

Results whose statement or proof uses this declaration.