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Mathlib/Combinatorics/SimpleGraph/Extremal Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -13,8 +13,8 @@ This file introduces basic definitions for extremal graph theory, including extr
1313
1414## Main definitions
1515
16- * `SimpleGraph.IsExtremal` is the predicate that `G` satisfies `p` and any `H` satisfying `p` has
17- at most as many edges as `G `.
16+ * `SimpleGraph.IsExtremal` is the predicate that `G` has the maximum number of edges of any simple
17+ graph, with fixed vertices, satisfying `p `.
1818
1919* `SimpleGraph.extremalNumber` is the maximum number of edges in a `H`-free simple graph on `n`
2020 vertices.
@@ -33,7 +33,7 @@ section IsExtremal
3333variable {V : Type *} [Fintype V] {G : SimpleGraph V} [DecidableRel G.Adj]
3434
3535/-- `G` is an extremal graph satisfying `p` if `G` has the maximum number of edges of any simple
36- graph satisfying `p`. -/
36+ graph, with fixed vertices, satisfying `p`. -/
3737def IsExtremal (G : SimpleGraph V) [DecidableRel G.Adj] (p : SimpleGraph V → Prop ) :=
3838 p G ∧ ∀ ⦃G' : SimpleGraph V⦄ [DecidableRel G'.Adj], p G' → #G'.edgeFinset ≤ #G.edgeFinset
3939
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