Geodesic
An improved bound on the largest induced forests for triangle-free planar graphs
Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 1.

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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. 
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     author = {Kowalik, Lukasz and Luzar, Borut and Skrekovski, Riste},
     title = {An improved bound on the largest induced forests for triangle-free planar graphs},
     journal = {Discrete mathematics & theoretical computer science},
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Kowalik, Lukasz; Luzar, Borut; Skrekovski, Riste. An improved bound on the largest induced forests for triangle-free planar graphs. Discrete mathematics & theoretical computer science, Tome 12 (2010) no. 1. doi : 10.46298/dmtcs.487. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.487/

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