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Theorems · Theorem · combinatorics

SimpleGraph.Walk.IsCycle.map

∀ {V : Type u} {V' : Type v} {G : SimpleGraph V} {G' : SimpleGraph V'} {f : G →g G'} {u : V} {p : G.Walk u u},
  Function.Injective ⇑f → p.IsCycle → (SimpleGraph.Walk.map f p).IsCycle

Alias of the reverse direction of SimpleGraph.Walk.isCycle_map_iff_of_injective.

Defined in
Mathlib.Combinatorics.SimpleGraph.Paths
Cited by
3 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
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Around this declaration

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

SimpleGraph.IsAcyclic.comap · cited by 4IsAcyclic.comapSimpleGraph.IsContained.egirth_le · cited by 2IsContained.egirth_leSimpleGraph.Walk.IsHamiltonianCycle.map · cited by 1IsHamiltonianCycle.mapDFunLike.coe · cited by 62936DFunLike.coeSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.Walk · cited by 915SimpleGraph.WalkSimpleGraph.Hom · cited by 139SimpleGraph.HomSimpleGraph.Walk.IsCycle · cited by 91Walk.IsCycleSimpleGraph.Walk.map · cited by 66Walk.mapSimpleGraph.Walk.isCycle_map_iff_of_injective · cited by 4Walk.isCycle_map_iff_of_i…IsCycle.mapCITED BYCITES

Cites8

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

Cited by3

Results whose statement or proof uses this declaration.