Hamiltonicity of random graphs produced by 2-processes

  • Authors:

  • András Telcs;Nicholas Wormald;Sanming Zhou

  • Affiliations:

  • Department of Computer Science and Information Theory, Budapest University of Technology and Economics, 1117 Budapest, Hungary;Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada;Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2007

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Abstract

Suppose that a random graph begins with n isolated vertices and evolves by edges being added at random, conditional upon all vertex degrees being at most 2. The final graph is usually 2-regular, but is not uniformly distributed. Some properties of this final graph are already known, but the asymptotic probability of being a Hamilton cycle was not known. We answer this question along with some related questions about cycles arising in the process. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007