Theorems · Definition · combinatorics
SimpleGraph.induce
{V : Type u_1} → (s : Set V) → SimpleGraph V → SimpleGraph ↑sRestrict a graph to the vertices in the set s, deleting all edges incident to vertices
outside the set. This is a wrapper around SimpleGraph.comap.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 80 results in Mathlib
- Foundations
- Depth 11 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.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- Function.Embedding.subtypeproof · cited by 128
- SimpleGraph.comapproof · cited by 29
Cited by95
Results whose statement or proof uses this declaration.
- SimpleGraph.ComponentComplproof · cited by 29
- SimpleGraph.componentComplMkproof · cited by 15
- SimpleGraph.ConnectedComponent.toSimpleGraphproof · cited by 14
- SimpleGraph.Walk.inducestatement · cited by 9
- SimpleGraph.induceHomstatement · cited by 7
- SimpleGraph.Embedding.inducestatement · cited by 6
- SimpleGraph.induceHomOfLEstatement · cited by 5
- SimpleGraph.induce_eq_coe_induce_topstatement · cited by 4
- SimpleGraph.connected_induce_iffstatement · cited by 4
- SimpleGraph.ComponentCompl.indproof · cited by 4
- SimpleGraph.Iso.inducestatement · cited by 3
- SimpleGraph.degree_induce_of_neighborSet_subsetstatement and proof · cited by 3