Packing vertices and edges in random regular graphs

  • Authors:

  • Mihalis Beis;William Duckworth;Michele Zito

  • Affiliations:

  • Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom;Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia;Department of Computer Science, University of Liverpool, Liverpool L69 3BX, United Kingdom

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2008

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Abstract

In 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 upper bounds on the maximal sizes of these sets. The lower bounds are proved by analyzing a class of algorithms that return feasible solutions for the given problems. The analysis uses the differential equation method proposed by Wormald [Lectures on Approximation and Randomized Algorithms, PWN, Wassaw, 1999, pp. 239–298]. The upper bounds are proved by direct combinatorial means. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008