Beis, MihalisDuckworth, WilliamZito, Michele2015-12-081042-9832http://hdl.handle.net/1885/31797In this paper we consider the problem of finding large collections of vertices and edges satisfying particular separation properties in random regular graphs of degree r, for each fixed r ≥ 3. We prove both constructive lower bounds and combinatorial upKeywords: Algorithms; Independent sets; Matchings; Random graphs200810.1002/rsa.201652015-12-08