FormalConjectures.WrittenOnTheWallII.GraphConjecture40

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import FormalConjecturesUtil

Written on the Wall II - Conjecture 40

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



namespace WrittenOnTheWallII.GraphConjecture40


open SimpleGraph


variable {α : Type*} [Fintype α] [DecidableEq α] [Nontrivial α] (G : SimpleGraph α)

WOWII Conjecture 40

For a nontrivial connected graph G the size f(G) of a largest induced forest satisfies f(G) ≥ ceil((p(G) + b(G) + 1)/2) where p(G) is the path cover number and b(G) is the largest induced bipartite subgraph size.

@[category research open, AMS 5]
theorem declaration uses 'sorry'conjecture40 (h_conn : G.Connected) (h_nontrivial : 1 < Fintype.card α) :
    ⌈(((pathCoverNumber G : ℝ) + b G + 1) / 2)⌉ ≤  G.largestInducedForestSize := byα:Type u_1inst✝²:Fintype αinst✝¹:DecidableEq αinst✝:Nontrivial αG:SimpleGraph αh_conn:G.Connectedh_nontrivial:1 < Fintype.card α⊢ ⌈(↑G.pathCoverNumber + G.b + 1) / 2⌉ ≤ ↑G.largestInducedForestSize
  sorryAll goals completed! 🐙


end WrittenOnTheWallII.GraphConjecture40