Theorems · Theorem · combinatorics
SimpleGraph.exists_isExtremal_iff_exists
∀ {V : Type u_1} [inst : Fintype V] (p : SimpleGraph V → Prop), (∃ G x, G.IsExtremal p) ↔ ∃ G, p GIf one simple graph satisfies p, then there exists an extremal graph satisfying p.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- Sym2proof · cited by 737
- SimpleGraph.edgeSetproof · cited by 199
- SimpleGraph.edgeFinsetproof · cited by 116
- SimpleGraph.IsExtremalstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.exists_isExtremal_freeproof · cited by 0