Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.Hom.comp

{V : Type u_1} →
  {W : Type u_2} →
    {X : Type u_3} → {G : SimpleGraph V} → {G' : SimpleGraph W} → {G'' : SimpleGraph X} → G' →g G'' → G →g G' → G →g G''

Composition of graph homomorphisms.

Defined in
Mathlib.Combinatorics.SimpleGraph.Maps
Cited by
20 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.Copy.comp · cited by 5Copy.compSimpleGraph.Coloring.sumLeft · cited by 3Coloring.sumLeftSimpleGraph.Coloring.sumRight · cited by 3Coloring.sumRightSimpleGraph.Colorable.mono_left · cited by 2Colorable.mono_leftSimpleGraph.Copy.range_toSubgraph · cited by 2Copy.range_toSubgraphSimpleGraph.Iso.symm_toHom_comp_toHom · cited by 1Iso.symm_toHom_comp_toHomSimpleGraph.Subgraph.map_comp · cited by 1Subgraph.map_compSimpleGraph.Coloring.comap · cited by 1Coloring.comapSimpleGraph.ConnectedComponent.map_comp · cited by 1ConnectedComponent.map_co…SimpleGraph.Coloring.surjOn_of_card_le_isClique · cited by 1Coloring.surjOn_of_card_l…SimpleGraph.induceHom_comp · cited by 1SimpleGraph.induceHom_compSimpleGraph.recolorOfEmbedding · cited by 1SimpleGraph.recolorOfEmbe…SimpleGraph.Hom.comp_assoc · cited by 0Hom.comp_assocSimpleGraph.Hom.comp_comap_ofLE · cited by 0Hom.comp_comap_ofLESimpleGraph.Hom.comp_id · cited by 0Hom.comp_idSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Hom · cited by 139SimpleGraph.HomRelHom.comp · cited by 7RelHom.compHom.compCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.