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module
public import Mathlib.Algebra.Order.Archimedean.Real.Basic
public import Mathlib.Combinatorics.SimpleGraph.Acyclic@[expose] public sectionnamespace SimpleGraphvariable {α : Type*} [Fintype α] [DecidableEq α]open Finset List
Ls G is the maximum number of leaves over all spanning trees of G.
It is defined to be 0 when G is not connected.
noncomputable def Ls (G : SimpleGraph α) [DecidableRel G.Adj] : ℝ :=
open scoped Classical in
letI spanningTrees := { T : Subgraph G | T.IsSpanning ∧ IsTree T.coe }
letI leaves (T : Subgraph G) := T.verts.toFinset.filter (fun v => T.degree v = 1)
letI num_leaves (T : Subgraph G) := (leaves T).card
sSup (Set.image (fun T => (num_leaves T : ℝ)) spanningTrees)end SimpleGraph