Theorems · Theorem · combinatorics
SimpleGraph.card_edgeFinset_le_extremalNumber
∀ {V : Type u_1} {W : Type u_2} {G : SimpleGraph V} {H : SimpleGraph W} [inst : Fintype V]
[inst_1 : DecidableRel G.Adj], H.Free G → G.edgeFinset.card ≤ SimpleGraph.extremalNumber (Fintype.card V) HIf G is H-free, then G has at most extremalNumber (card V) H edges.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.cardstatement and proof · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.filterproof · cited by 949
- IsEmptyproof · cited by 759
- Sym2statement and proof · cited by 737
- Finset.supproof · cited by 530
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.isExtremal_free_iffproof · cited by 2
- SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumberproof · cited by 1
- SimpleGraph.extremalNumber_congrproof · cited by 1
- SimpleGraph.IsContained.of_extremalNumber_lt_card_edgeFinsetproof · cited by 1
- SimpleGraph.eventually_isContained_of_card_edgeFinsetproof · cited by 1
- SimpleGraph.zarankiewicz_le_extremalNumberproof · cited by 0