Induced forests in planar bipartite graphs

Determine whether every planar bipartite graph on n vertices contains an induced forest on at least 5n/8 vertices.

Background

The paper discusses the forest number, defined as the maximum order of an induced forest in a graph, and places its results in the context of earlier work on induced forests in planar and bipartite graphs. It reports that Akiyama and Watanabe, and independently Albertson and Haas, proposed the 5n/8 lower bound for planar bipartite graphs. The cited statement is presented as a conjecture and is not resolved by the results proved in this paper, which concern balanced bipartite graphs under minimum-degree conditions.