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

François Dross, Mickael Montassier, Alexandre Pinlou

We prove that every triangle-free planar graph of order $n$ and size $m$ has an induced linear forest with at least $\frac{9n-2m}{11}$ vertices, and thus at least $\frac{5n + 8}{…