An improved bound on the largest induced forests for triangle-free planar graphs
Authors: Kowalik, Lukasz and Luzar, Borut and Skrekovski, Riste
We proved that every planar triangle-free graph of order n has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of Salavatipour (2006). We also pose some questions regarding planar graphs of higher girth.