The connectivity threshold for the min-degree random graph process

  • Authors:

  • Mihyun Kang;Youngmee Koh;Sangwook Ree;Tomasz Łuczak

  • Affiliations:

  • Department of Computer Science, Humboldt University Berlin, Unter den Linden 6, 10099 Berlin, Germany;Department of Mathematics, University of Suwon, Suwon, P.O.Box 77, Kyungki-do 440-600, South Korea;Department of Mathematics, University of Suwon, Suwon, P.O.Box 77, Kyungki-do 440-600, South Korea;Department of Discrete Mathematics, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland

  • Venue:
  • Random Structures & Algorithms
  • Year:
  • 2006

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Abstract

Let 𝒢n = {Gmin(n, M)}M≥0 denote a min-degree random multigraph process in which Gmin(n, M + 1) is obtained from Gmin(n, M) by connecting a randomly chosen vertex of a minimum degree with another vertex of the multigraph. We study the probability that the random multigraph Gmin(n, M) is connected. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006