Maximum acyclic and fragmented sets in regular graphs

  • Authors:

  • Penny Haxell;Oleg Pikhurko;Andrew Thomason

  • Affiliations:

  • Department of Combinatorics and Optimization University of Waterloo Waterloo, Ontario N2L 3G1, Canada;Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, Pennsylvania 15213;Centre for Mathematical Sciences Cambridge University Cambridge CB3 0WB, United Kingdom

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

We show that a typical d-regular graph G of ordern does not contain an induced forest with around2Ind/d vertices, when n d 1, this bound being best possible because of aresult of Frieze and Luczak [6]. We then deduce an affirmativeanswer to an open question of Edwards and Farr (see [4]) aboutfragmentability, which concerns large subgraphs with components ofbounded size. An alternative, direct answer to the question is alsogiven. © 2007 Wiley Periodicals, Inc. J Graph Theory 57:149156, 2008