Theorems · Definition · combinatorics
SimpleGraph.Subgraph.induce
{V : Type u} → {G : SimpleGraph V} → G.Subgraph → Set V → G.SubgraphThe induced subgraph of a subgraph. The expectation is that s ⊆ G'.verts for the usual
notion of an induced subgraph, but, in general, s is taken to be the new vertex set and edges
are induced from the subgraph G'.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.Adjproof · cited by 147
Cited by36
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.induce_adjstatement and proof · cited by 17
- SimpleGraph.Subgraph.induce_vertsstatement and proof · cited by 15
- SimpleGraph.Subgraph.deleteVertsproof · cited by 15
- SimpleGraph.ConnectedComponent.toSubgraphproof · cited by 5
- SimpleGraph.Subgraph.induce_monostatement · cited by 4
- SimpleGraph.induce_eq_coe_induce_topstatement and proof · cited by 4
- SimpleGraph.Subgraph.le_induce_top_vertsstatement · cited by 4
- SimpleGraph.connected_induce_iffstatement and proof · cited by 4
- SimpleGraph.Subgraph.le_induce_unionstatement · cited by 3
- SimpleGraph.Subgraph.subgraphOfAdj_eq_inducestatement and proof · cited by 2
- SimpleGraph.Subgraph.top_induce_pair_connected_of_adjstatement · cited by 2
- SimpleGraph.Subgraph.induce_mono_rightstatement · cited by 2