Theorems · Theorem · combinatorics
SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton
∀ {α : Type u_1} {G : SimpleGraph α},
G.EdgeDisjointTriangles ↔ ∀ ⦃e : Sym2 α⦄, ¬e.IsDiag → {s | s ∈ G.cliqueSet 3 ∧ e ∈ s.sym2}.Subsingleton- Cited by
- 1 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- SimpleGraphstatement and proof · cited by 3,072
- Set.extproof · cited by 2,266
- SimpleGraph.Adjproof · cited by 1,346
- Sym2statement and proof · cited by 737
- Finset.extproof · cited by 565
- Iff.notproof · cited by 489
- Sym2.mkproof · cited by 332
- Set.Subsingletonstatement and proof · cited by 276
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.EdgeDisjointTriangles.mem_sym2_subsingletonproof · cited by 1