Theorems · Definition · combinatorics
SimpleGraph.extremalNumber
ℕ → {W : Type u_1} → SimpleGraph W → ℕThe extremal number of a natural number n and a simple graph H is the maximum number of
edges in a H-free simple graph on n vertices.
If H is contained in all simple graphs on n vertices, then this is 0.
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.univproof · cited by 3,473
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- Finset.filterproof · cited by 949
- Finset.supproof · cited by 530
- SimpleGraph.edgeFinsetproof · cited by 116
- SimpleGraph.Freeproof · cited by 39
Cited by24
Results whose statement or proof uses this declaration.
- SimpleGraph.card_edgeFinset_le_extremalNumberstatement · cited by 6
- SimpleGraph.turanDensityproof · cited by 6
- SimpleGraph.extremalNumber_le_iffstatement · cited by 4
- SimpleGraph.extremalNumber_of_fintypeCard_eqstatement · cited by 3
- SimpleGraph.antitoneOn_extremalNumber_div_choose_twostatement and proof · cited by 3
- SimpleGraph.extremalNumber_le_iff_of_nonnegstatement and proof · cited by 2
- SimpleGraph.isExtremal_free_iffstatement and proof · cited by 2
- SimpleGraph.isGLB_turanDensitystatement and proof · cited by 2
- SimpleGraph.IsContained.of_extremalNumber_lt_card_edgeFinsetstatement and proof · cited by 1
- SimpleGraph.eventually_isContained_of_card_edgeFinsetproof · cited by 1
- SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumberstatement and proof · cited by 1
- SimpleGraph.card_edgeFinset_of_isExtremal_freestatement · cited by 1