%0 Journal Article
%T Large induced forests in planar graphs with girth 4 or 5
%A Fran£żois Dross
%A Mickael Montassier
%A Alexandre Pinlou
%J Computer Science
%D 2014
%I arXiv
%X We give here some new lower bounds on the order of a largest induced forest in planar graphs with girth $4$ and $5$. In particular we prove that a triangle-free planar graph of order $n$ admits an induced forest of order at least $\frac{6n+7}{11}$ , improving the lower bound of Salavatipour [M. R. Salavatipour, Large induced forests in triangle-free planar graphs, Graphs and Combinatorics, 22:113-126, 2006]. We also prove that a planar graph of order $n$ and girth at least $5$ admits an induced forest of order at least $\frac{44n+50}{69}$.
%U http://arxiv.org/abs/1409.1348v1