A lower bound on the order of the largest induced linear forest in triangle-free planar graphs

Abstract We prove that every triangle-free planar graph of order n and size m has an induced linear forest with at least 9 n − 2 m 11 vertices, and thus at least 5 n + 8 11 vertices. Furthermore, we show that there are triangle-free planar graphs on n vertices whose largest induced linear forest has order ⌈ n 2 ⌉ + 1 .