Maximum acyclic and fragmented sets in regular graphs

Abstract

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)
DOI: 10.1002/jgt.20271

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Cite this paper

@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} }