Theorems · Definition · combinatorics
SimpleGraph.Hom
{V : Type u_1} → {W : Type u_2} → SimpleGraph V → SimpleGraph W → Type (max u_1 u_2)A graph homomorphism is a map on vertex sets that respects adjacency relations.
The notation G →g G' represents the type of graph homomorphisms.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Maps
- Cited by
- 139 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjproof · cited by 1,346
- RelHomproof · cited by 49
Cited by177
Results whose statement or proof uses this declaration.
- SimpleGraph.Walk.mapstatement and proof · cited by 66
- SimpleGraph.Coloringproof · cited by 44
- SimpleGraph.Hom.ofLEstatement · cited by 27
- SimpleGraph.Subgraph.mapstatement and proof · cited by 24
- SimpleGraph.Hom.map_adjstatement and proof · cited by 21
- SimpleGraph.Hom.compstatement and proof · cited by 20
- SimpleGraph.Subgraph.homstatement · cited by 18
- SimpleGraph.Embedding.toHomstatement · cited by 17
- SimpleGraph.Reachable.mapstatement and proof · cited by 14
- SimpleGraph.Copy.toHomstatement · cited by 14
- SimpleGraph.Subgraph.map_vertsstatement and proof · cited by 13
- SimpleGraph.Iso.toHomstatement · cited by 13