We show that a typical d-regular graph G of order n does not contain an induced forest with around 2 ln d d n vertices, when n d 1, this bound being best possible because of a result of Frieze and Łuczak [6]. We then deduce an affirmative answer to an open question of Edwards and Farr (see [4]) about fragmentability, which concerns large subgraphs with… (More)

@article{Haxell2008MaximumAA,
title={Maximum acyclic and fragmented sets in regular graphs},
author={Penny E. Haxell and Oleg Pikhurko and Andrew Thomason},
journal={Journal of Graph Theory},
year={2008},
volume={57},
pages={149-156}
}