FormalConjectures.WrittenOnTheWallII.GraphConjecture6

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import FormalConjecturesUtil

Written on the Wall II - Conjecture 6

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



open SimpleGraph


namespace WrittenOnTheWallII.GraphConjecture6

variable {α : Type*} [Fintype α] [DecidableEq α] [Nontrivial α]

WOWII Conjecture 6

For a connected graph G we have Ls(G) ≥ 1 + n(G) - m(G) - a(G) where a(G) is defined via independent sets.

@[category research solved, AMS 5]
theorem declaration uses 'sorry'conjecture6 (G : SimpleGraph α) [DecidableRel G.Adj] (h_conn : G.Connected) :
    1 + (Fintype.card α : ℝ) - matchingNumber G - α(G) ≤ Ls G := byα:Type u_1inst✝³:Fintype αinst✝²:DecidableEq αinst✝¹:Nontrivial αG:SimpleGraph αinst✝:DecidableRel G.Adjh_conn:G.Connected⊢ 1 + ↑(Fintype.card α) - G.matchingNumber - ↑α(G) ≤ G.Ls
  sorryAll goals completed! 🐙


end WrittenOnTheWallII.GraphConjecture6