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 is open since 1979, states that $a(G) \geq \frac{n}{2}$ for all simple planar graphs $G$. 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 all planar multigraphs $M$ 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 planar graphs, assuming that it holds, would imply the lower bound $a(M) \geq \frac{n-k}{2}$ for planar 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 $G$ 中最大诱导森林的顶点数。自1979年提出以来一直悬而未决的Albertson-Berman猜想断言：对于所有简单平面图 $G$，有 $a(G) \geq \frac{n}{2}$。本文证明，该问题在多重图（允许平行边）情形下的版本可简化为简单平面图的独立数问题。具体而言，我们证明了对于所有平面多重图 $M$，有 $a(M) \geq \frac{n}{4}$，且该下界是紧的。随后，我们研究了具有平行边的顶点对数量（记为 $k$）较小的情况。特别地，我们证明了 $a(M) \geq \frac{2}{5}n-\frac{k}{10}$ 这一下界，并指出若Albertson-Berman猜想对简单平面图成立，则可推导出平面多重图的下界 $a(M) \geq \frac{n-k}{2}$——当 $k$ 较小时该下界优于通用下界。最后，我们研究了禁止平面多重图存在 $2$-面的问题变体，这是本文引入的主要非平凡问题。针对该无 $2$-面的变体，我们证明了 $a(M) \geq \frac{3}{10}n+\frac{7}{30}$ 的下界，并构造了一个满足 $a(M)=\frac{3}{7}n+\frac{4}{7}$ 的无穷多重图序列。