Written on the Wall II - Conjecture 40
Written on the Wall II - Conjecture 40
Inferred from the community field; finer classification has not been reviewed.
Problem statement
conjecture40
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.
Lean 4
Formal statement
Lean 4/-
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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](http://cms.dt.uh.edu/faculty/delavinae/research/wowII/)
-/
namespace WrittenOnTheWallII.GraphConjecture40
open SimpleGraph
variable {α : Type*} [Fintype α] [DecidableEq α] [Nontrivial α] (G : SimpleGraph α)
/--
WOWII [Conjecture 40](http://cms.dt.uh.edu/faculty/delavinae/research/wowII/)
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 conjecture40 (h_conn : G.Connected) (h_nontrivial : 1 < Fintype.card α) :
⌈(((pathCoverNumber G : ℝ) + b G + 1) / 2)⌉ ≤ G.largestInducedForestSize := by
sorry
end WrittenOnTheWallII.GraphConjecture40
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Background
Source snapshot inspected on 10 September 2026. Subsequent research status and the accuracy of source formalizations have not been independently certified.
Fixed commit b82b08faa9006484021c12005ab41287fb2ffb69. This file contains 1 source-labeled research-open declarations. Other declarations in the attached file can be definitions, solved results or tests. The file is preserved as source material; it has not been compiled or proved by this import.
Copyright The Formal Conjectures Authors. Code: Apache-2.0; other original material: CC BY 4.0. Third-party sources retain their own licenses. Original source files and notices preserved.
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