Mikhail Makarov

A counterexample to the Albertson-Berman conjecture about induced forests in planar graphs

For a graph $G$, denote by $a(G)$ the number of vertices in the largest induced forest in $G$. The Albertson-Berman conjecture, which had been open since 1979, states that $a(G) \geq \frac{n}{2}$ for every simple planar graph $G$ on $n$ vertices. Although the Albertson-Berman conjecture was recently resolved in the neg...