Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.ConnectedComponent.supp

{V : Type u} → {G : SimpleGraph V} → G.ConnectedComponent → Set V

The set of vertices in a connected component of a graph.

Defined in
Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected
Cited by
42 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms

Around this declaration

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

SimpleGraph.ConnectedComponent.toSimpleGraph · cited by 14ConnectedComponent.toSimp…SimpleGraph.oddComponents · cited by 10SimpleGraph.oddComponentsSimpleGraph.ConnectedComponent.toSubgraph · cited by 5ConnectedComponent.toSubg…SimpleGraph.ConnectedComponent.mem_supp_iff · cited by 4ConnectedComponent.mem_su…SimpleGraph.ConnectedComponent.eq_of_common_vertex · cited by 2ConnectedComponent.eq_of_…SimpleGraph.ConnectedComponent.mem_supp_congr_adj · cited by 2ConnectedComponent.mem_su…SimpleGraph.ConnectedComponent.nonempty_supp · cited by 2ConnectedComponent.nonemp…SimpleGraph.ConnectedComponent.reachable_of_mem_supp · cited by 2ConnectedComponent.reacha…SimpleGraph.ConnectedComponent.supp_injective · cited by 2ConnectedComponent.supp_i…SimpleGraph.ConnectedComponent.Represents.exists_inter_eq_singleton · cited by 2Represents.exists_inter_e…SimpleGraph.ConnectedComponent.adj_spanningCoe_toSimpleGraph · cited by 1ConnectedComponent.adj_sp…SimpleGraph.ConnectedComponent.biUnion_supp_eq_supp · cited by 1ConnectedComponent.biUnio…SimpleGraph.ConnectedComponent.Represents.ncard_sdiff_of_mem · cited by 1Represents.ncard_sdiff_of…SimpleGraph.ConnectedComponent.Represents.ncard_sdiff_of_notMem · cited by 1Represents.ncard_sdiff_of…SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSupp · cited by 1Connected.exists_verts_eq…Set · cited by 53352SetSet.ofPred · cited by 6101Set.ofPredSimpleGraph · cited by 3072SimpleGraphSimpleGraph.ConnectedComponent · cited by 86SimpleGraph.ConnectedComp…SimpleGraph.connectedComponentMk · cited by 40SimpleGraph.connectedComp…ConnectedComponent.suppCITED BYCITES

Cites5

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

Cited by46

Results whose statement or proof uses this declaration.