Theorems · Definition · combinatorics
SimpleGraph.IsExtremal
{V : Type u_1} → [Fintype V] → (G : SimpleGraph V) → [DecidableRel G.Adj] → (SimpleGraph V → Prop) → PropG is an extremal graph satisfying p if G has the maximum number of edges of any simple
graph, with fixed vertices, satisfying p.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 65 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- Finset.cardproof · cited by 2,327
- SimpleGraph.Adjstatement and proof · cited by 1,346
- SimpleGraph.edgeFinsetproof · cited by 116
Cited by10
Results whose statement or proof uses this declaration.
- SimpleGraph.IsTuranMaximalproof · cited by 19
- SimpleGraph.isExtremal_free_iffstatement · cited by 2
- SimpleGraph.isExtremal_top_free_iff_isTuranMaximalstatement · cited by 2
- SimpleGraph.card_edgeFinset_of_isExtremal_freestatement and proof · cited by 1
- SimpleGraph.exists_isExtremal_iff_existsstatement and proof · cited by 1
- SimpleGraph.isExtremal_top_free_turanGraphstatement · cited by 1
- SimpleGraph.IsExtremal.le_iff_eqstatement and proof · cited by 1
- SimpleGraph.exists_isExtremal_freestatement · cited by 0
- SimpleGraph.IsExtremal.congr_simpstatement and proof · cited by 0
- SimpleGraph.IsExtremal.propstatement and proof · cited by 0