Induced Forests in Bipartite Planar Graphs

TL;DR

This paper proves a new lower bound on the size of induced forests in bipartite planar graphs using the discharging method, improving previous conjectures and results.

Contribution

It establishes a tighter lower bound of rac{4n+3}{7}or induced forests in bipartite planar graphs, advancing understanding of their structural properties.

Findings

Every bipartite planar graph on n vertices has an induced forest of at least rac{4n+3}{7}vertices.

The discharging method effectively proves bounds on induced subgraphs in planar graphs.

Improves upon the previous conjecture of a rac{5n}{8}orest size.

Abstract

Akiyama and Watanabe conjectured that every simple planar bipartite graph on $n$ vertices contains an induced forest on at least $5n/8$ vertices. We apply the discharging method to show that every simple bipartite planar graph on $n$ vertices contains an induced forest on at least $\lceil (4n+3)/7 \rceil$ vertices.