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Theorems · Theorem · combinatorics

SimpleGraph.Hom.map_adj

∀ {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {G' : SimpleGraph W} (f : G →g G') {v w : V},
  G.Adj v w → G'.Adj (f v) (f w)
Defined in
Mathlib.Combinatorics.SimpleGraph.Maps
Cited by
21 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

SimpleGraph.Hom.le_comap · cited by 3Hom.le_comapSimpleGraph.Walk.map_append · cited by 2Walk.map_appendSimpleGraph.Hom.injective_of_top_hom · cited by 2Hom.injective_of_top_homSimpleGraph.Walk.toSubgraph_map · cited by 2Walk.toSubgraph_mapSimpleGraph.Walk.transfer_eq_map_ofLE · cited by 1Walk.transfer_eq_map_ofLESimpleGraph.Walk.map_injective_of_injective · cited by 1Walk.map_injective_of_inj…SimpleGraph.Walk.IsHamiltonianCycle.map · cited by 1IsHamiltonianCycle.mapSimpleGraph.Hom.apply_mem_neighborSet · cited by 1Hom.apply_mem_neighborSetSimpleGraph.turanGraph_cliqueFree · cited by 1SimpleGraph.turanGraph_cl…SimpleGraph.map_subgraphOfAdj · cited by 1SimpleGraph.map_subgraphO…SimpleGraph.Walk.reverse_map · cited by 1Walk.reverse_mapSimpleGraph.Walk.map.eq_def · cited by 0map.eq_defSimpleGraph.nonempty_hom_of_forall_finite_subgraph_hom · cited by 0SimpleGraph.nonempty_hom_…SimpleGraph.Walk.getVert_map · cited by 0Walk.getVert_mapSimpleGraph.completeBipartiteGraph_isContained_iff · cited by 0SimpleGraph.completeBipar…DFunLike.coe · cited by 62936DFunLike.coeSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.Hom · cited by 139SimpleGraph.HomRelHom.map_rel' · cited by 4RelHom.map_rel'Hom.map_adjCITED BYCITES

Cites5

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

Cited by21

Results whose statement or proof uses this declaration.