For a graph $G$ on $n$ vertices, denote by $a(G)$ the number of vertices in the largest induced forest in $G$. The Albertson-Berman conjecture, which has been open since 1979, states that $a(G) \geq \frac{n}{2}$ for every simple planar graph $G$. We show that the version of this problem for multigraphs (allowing parallel edges) is easily reduced to the problem about the independence number of simple planar graphs. Specifically, we prove that $a(M) \geq \frac{n}{4}$ for every planar multigraph $M$ and that this lower bound is tight. Then, we study the case when the number of pairs of vertices with parallel edges, which we denote by $k$, is small. In particular, we prove the lower bound $a(M) \geq \frac{2}{5}n-\frac{k}{10}$ and that the Albertson-Berman conjecture for simple graphs, assuming that it holds, would imply the lower bound $a(M) \geq \frac{n-k}{2}$ for multigraphs, which would be better than the general lower bound when $k$ is small. Finally, we study the variant of the problem where the plane multigraphs are prohibited from having $2$-faces, which is the main non-trivial problem that we introduce in this article. For that variant without $2$-faces, we prove the lower bound $a(M) \geq \frac{3}{10}n+\frac{7}{30}$ and give a construction of an infinite sequence of multigraphs with $a(M)=\frac{3}{7}n+\frac{4}{7}$.

翻译：对于具有$n$个顶点的图$G$，记$a(G)$为$G$中最大导出森林的顶点数。自1979年以来一直未解决的Albertson-Berman猜想指出：对于每个简单平面图$G$，有$a(G) \geq \frac{n}{2}$。我们证明，该问题在多重图（允许平行边）情形下可简化为简单平面图的独立数问题。具体地，我们证明对于每个平面多重图$M$，有$a(M) \geq \frac{n}{4}$，且该下界是紧的。接着，我们研究当具有平行边的顶点对数量（记为$k$）较小时的情形。特别地，我们证明了下界$a(M) \geq \frac{2}{5}n-\frac{k}{10}$，并指出若Albertson-Berman猜想成立，则对于简单图，它将导出多重图的下界$a(M) \geq \frac{n-k}{2}$，当$k$较小时该下界优于一般情形的下界。最后，我们研究该问题的一个变体——禁止平面多重图包含$2$面，这是本文引入的主要非平凡问题。针对无$2$面的变体，我们证明下界$a(M) \geq \frac{3}{10}n+\frac{7}{30}$，并构造一个满足$a(M)=\frac{3}{7}n+\frac{4}{7}$的无限多重图序列。