SURVEY ARTICLE: The forest number in several classes of regular graphs

For a graph $G$ and $F ⊆ V (G),$ if $\langle F\rangle$ is acyclic, then $F$ is said to be an induced forest of $G.$ The size of a maximum induced forest of $G$ is called the forest number of $G$ and is denoted by $\mathsf{f}(G)$. The purpose of this paper is to provide a review of recent results and open problems on the forest number of graphs and in some classes of graphs.