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Theorems · Theorem · combinatorics

SimpleGraph.isNClique_map_iff

∀ {α : Type u_1} {β : Type u_2} {G : SimpleGraph α} {n : ℕ},
  1 < n →
    ∀ {t : Finset β} {f : α ↪ β}, (SimpleGraph.map (⇑f) G).IsNClique n t ↔ ∃ s, G.IsNClique n s ∧ Finset.map f s = t
Defined in
Mathlib.Combinatorics.SimpleGraph.Clique
Cited by
1 results in Mathlib
Foundations
Depth 68 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.cliqueFree_map_iff · cited by 0SimpleGraph.cliqueFree_ma…DFunLike.coe · cited by 62936DFunLike.coeFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeSimpleGraph · cited by 3072SimpleGraphFinset.card · cited by 2327Finset.cardFunction.Embedding · cited by 988Function.EmbeddingFinset.map · cited by 747Finset.mapLE.le.not_gt · cited by 189le.not_gtFinset.card_map · cited by 114Finset.card_mapSimpleGraph.IsClique · cited by 76SimpleGraph.IsCliqueSimpleGraph.IsNClique · cited by 64SimpleGraph.IsNCliqueSimpleGraph.map · cited by 49SimpleGraph.mapSimpleGraph.IsNClique.card_eq · cited by 17IsNClique.card_eqSimpleGraph.IsNClique.isClique · cited by 14IsNClique.isCliqueSimpleGraph.isNClique_iff · cited by 5SimpleGraph.isNClique_iffSimpleGraph.isNClique_map_iffCITED BYCITES

Cites16

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Cited by1

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