A 15/31 Counterexample Family to the Albertson–Berman Conjecture

We disprove the Albertson–Berman conjecture (1979), which asserts that every n-vertex planar graph has an induced forest on at least n/2 vertices. We exhibit an explicit 31-vertex plane triangulation T whose maximum induced forest has 15 vertices. Moreover, for every k >= 2, we construct a simple planar graph M_k on 31k vertices with minimum degree 5 and maximum induced forest of exactly 15k vertices, giving the ratio 15/31 < 1/2. A self-contained Python verifier is included.

Correspondence: hdhehia@knou.ac.kr