A better bound on the largest induced forests in triangle-free planar graphs

Abstract

It is well-known that there exists a triangle-free planar graph of $n$ verticess such that the largest induced forest has size at most $\frac{5n}{8}$. Salavatipour proved that there is a forest of size at least $\frac{5n}{9.41}$ in any triangle-free planar graph of $n$ vertices. Dross, Montassier and Pinlou improved Salavatipour's bound to $\frac{5n}{9.17}$. In this work, we further improve the bound to $\frac{5n}{9}$. Our technique is inspired by the recent ideas from Lukot'ka, Maz{á}k and Zhu.

Fix an error in the statement of Theorem 1. Fix typos

References in corpus (1)

• Large induced forests in planar graphs with girth 4 or 5