Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.componentComplMk

{V : Type u} → {K : Set V} → (G : SimpleGraph V) → {v : V} → v ∉ K → G.ComponentCompl K

The connected component of v in G.induce Kᶜ.

Defined in
Mathlib.Combinatorics.SimpleGraph.Ends.Defs
Cited by
15 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound

Around this declaration

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

SimpleGraph.ComponentCompl.supp · cited by 6ComponentCompl.suppSimpleGraph.ComponentCompl.ind · cited by 4ComponentCompl.indSimpleGraph.ComponentCompl.subset_hom · cited by 3ComponentCompl.subset_homSimpleGraph.ComponentCompl.infinite_iff_in_all_ranges · cited by 2ComponentCompl.infinite_i…SimpleGraph.componentComplMk_mem · cited by 2SimpleGraph.componentComp…SimpleGraph.ComponentCompl.hom_eq_iff_le · cited by 1ComponentCompl.hom_eq_iff…SimpleGraph.ComponentCompl.hom_mk · cited by 1ComponentCompl.hom_mkSimpleGraph.ComponentCompl.mem_of_adj · cited by 1ComponentCompl.mem_of_adjSimpleGraph.ComponentCompl.exists_adj_boundary_pair · cited by 0ComponentCompl.exists_adj…SimpleGraph.ComponentCompl.exists_eq_mk · cited by 0ComponentCompl.exists_eq_…SimpleGraph.end_hom_mk_of_mk · cited by 0SimpleGraph.end_hom_mk_of…SimpleGraph.ComponentCompl.hom_eq_iff_not_disjoint · cited by 0ComponentCompl.hom_eq_iff…SimpleGraph.ComponentCompl.mem_supp_iff · cited by 0ComponentCompl.mem_supp_i…SimpleGraph.componentComplMk_eq_of_adj · cited by 0SimpleGraph.componentComp…SimpleGraph.componentComplMk_mem_hom · cited by 0SimpleGraph.componentComp…Set · cited by 53352SetSimpleGraph · cited by 3072SimpleGraphCompl.compl · cited by 2925Compl.complSimpleGraph.induce · cited by 80SimpleGraph.induceSimpleGraph.connectedComponentMk · cited by 40SimpleGraph.connectedComp…SimpleGraph.ComponentCompl · cited by 29SimpleGraph.ComponentComplSimpleGraph.componentComplMkCITED BYCITES

Cites6

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

Cited by16

Results whose statement or proof uses this declaration.