Theorems · Definition · combinatorics
SimpleGraph.Subgraph.hom
{V : Type u} → {G : SimpleGraph V} → (x : G.Subgraph) → x.coe →g GThere is an induced injective homomorphism of a subgraph of G into G.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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.
- Set.Elemstatement and proof · cited by 7,166
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Subgraphstatement and proof · cited by 326
- SimpleGraph.Subgraph.vertsstatement and proof · cited by 210
- SimpleGraph.Homstatement · cited by 139
- SimpleGraph.Subgraph.coestatement · cited by 89
Cited by22
Results whose statement or proof uses this declaration.
- SimpleGraph.Subgraph.coeSubgraphproof · cited by 10
- SimpleGraph.Subgraph.hom_applystatement and proof · cited by 6
- SimpleGraph.Subgraph.restrictproof · cited by 3
- SimpleGraph.Subgraph.coeSubgraph_adjproof · cited by 2
- SimpleGraph.Subgraph.hom_injectivestatement · cited by 2
- SimpleGraph.Copy.range_toSubgraphproof · cited by 2
- SimpleGraph.Subgraph.Connected.exists_verts_eq_connectedComponentSuppproof · cited by 1
- SimpleGraph.Subgraph.coeCopyproof · cited by 1
- SimpleGraph.Subgraph.map_hom_topstatement and proof · cited by 1
- SimpleGraph.ConnectedComponent.maximal_connected_toSubgraphproof · cited by 1
- SimpleGraph.Subgraph.preconnected_iff_forall_exists_walk_subgraphproof · cited by 1
- SimpleGraph.Subgraph.restrict_coeSubgraphproof · cited by 1