FormalConjectures.WrittenOnTheWallII.GraphConjecture1

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import FormalConjecturesUtil

Written on the Wall II - Conjecture 1

Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc


namespace WrittenOnTheWallII.GraphConjecture1


open SimpleGraph

WOWII Conjecture 1

For a simple connected graph G the maximum number of leaves of a spanning tree satisfies Ls(G) ≥ n(G) + 1 - 2·m(G) where n(G) counts vertices and m(G) is the size of a maximum matching.


@[category research solved, AMS 5]
theorem declaration uses 'sorry'conjecture1 {α : Type*} [Fintype α] [DecidableEq α] [Nontrivial α]
    (G : SimpleGraph α) [DecidableRel G.Adj] (h_conn : G.Connected) :
    (Fintype.card α : ℝ) + 1 - 2 * matchingNumber G ≤ (Ls G : ℝ) := byα:Type u_1inst✝³:Fintype αinst✝²:DecidableEq αinst✝¹:Nontrivial αG:SimpleGraph αinst✝:DecidableRel G.Adjh_conn:G.Connected⊢ ↑(Fintype.card α) + 1 - 2 * G.matchingNumber ≤ G.Ls
  sorryAll goals completed! 🐙


end WrittenOnTheWallII.GraphConjecture1