Theorems · Theorem · combinatorics
SimpleGraph.cliqueFree_iff
∀ {α : Type u_1} {G : SimpleGraph α} {n : ℕ}, G.CliqueFree n ↔ IsEmpty ((SimpleGraph.completeGraph (Fin n)).Copy G)- Defined in
- Mathlib.Combinatorics.SimpleGraph.Clique
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SimpleGraphstatement and proof · cited by 3,072
- IsEmptystatement · cited by 759
- SimpleGraph.CliqueFreestatement and proof · cited by 70
- SimpleGraph.Copystatement · cited by 49
- SimpleGraph.completeGraphstatement · cited by 49
- SimpleGraph.not_cliqueFree_iff_top_isContainedproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- SimpleGraph.completeMultipartiteGraph.not_cliqueFree_of_le_cardproof · cited by 3
- SimpleGraph.turanGraph_cliqueFreeproof · cited by 1
- SimpleGraph.cliqueFree_completeMultipartiteGraphproof · cited by 0
- SimpleGraph.cliqueFree_of_card_ltproof · cited by 0