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Theorems · Theorem · combinatorics

SimpleGraph.Hom.injective_of_top_hom

∀ {V : Type u_1} {W : Type u_2} {G' : SimpleGraph W} (f : ⊤ →g G'), Function.Injective ⇑f

Every graph homomorphism from a complete graph is injective.

Defined in
Mathlib.Combinatorics.SimpleGraph.Maps
Cited by
2 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

SimpleGraph.chromaticNumber_top · cited by 4SimpleGraph.chromaticNumb…SimpleGraph.chromaticNumber_top_eq_top_of_infinite · cited by 1SimpleGraph.chromaticNumb…DFunLike.coe · cited by 62936DFunLike.coeTop.top · cited by 9680Top.topSimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.Hom · cited by 139SimpleGraph.HomSimpleGraph.Hom.map_adj · cited by 21Hom.map_adjSimpleGraph.ne_of_adj · cited by 14SimpleGraph.ne_of_adjSimpleGraph.top_adj · cited by 5SimpleGraph.top_adjHom.injective_of_top_homCITED BYCITES

Cites8

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

Cited by2

Results whose statement or proof uses this declaration.