Theorems · Definition · combinatorics
SimpleGraph.componentComplMk
{V : Type u} → {K : Set V} → (G : SimpleGraph V) → {v : V} → v ∉ K → G.ComponentCompl KThe connected component of v in G.induce Kᶜ.
- 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SimpleGraphstatement and proof · cited by 3,072
- Compl.complproof · cited by 2,925
- SimpleGraph.induceproof · cited by 80
- SimpleGraph.connectedComponentMkproof · cited by 40
- SimpleGraph.ComponentComplstatement · cited by 29
Cited by16
Results whose statement or proof uses this declaration.
- SimpleGraph.ComponentCompl.suppproof · cited by 6
- SimpleGraph.ComponentCompl.indstatement and proof · cited by 4
- SimpleGraph.ComponentCompl.subset_homproof · cited by 3
- SimpleGraph.ComponentCompl.infinite_iff_in_all_rangesproof · cited by 2
- SimpleGraph.componentComplMk_memstatement · cited by 2
- SimpleGraph.ComponentCompl.hom_eq_iff_leproof · cited by 1
- SimpleGraph.ComponentCompl.hom_mkstatement · cited by 1
- SimpleGraph.ComponentCompl.mem_of_adjproof · cited by 1
- SimpleGraph.ComponentCompl.exists_adj_boundary_pairproof · cited by 0
- SimpleGraph.ComponentCompl.exists_eq_mkstatement · cited by 0
- SimpleGraph.end_hom_mk_of_mkstatement and proof · cited by 0
- SimpleGraph.ComponentCompl.hom_eq_iff_not_disjointproof · cited by 0