An improved bound on the largest induced forests for triangle-free planar graphs

Lukasz Kowalik (1) , Borut Luzar (2) , Riste Skrekovski (2)

1 Institute of Informatics [Warsaw]
2 FMF - Faculty of Mathematics and Physics [Ljubljana]

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.

Mots clés: Induced forest; Forest number; Decycling number

Domaines: Mathématique discrète [cs.DM]

Lukasz Kowalik, Borut Luzar, Riste Skrekovski. An improved bound on the largest induced forests for triangle-free planar graphs. Discrete Mathematics and Theoretical Computer Science, 2010, Vol. 12 no. 1 (1), pp.87-100. ⟨10.46298/dmtcs.487⟩. ⟨hal-00990440⟩