Uncover Low Degree Vertices and Minimise the Mess: Independent Sets in Random Regular Graphs

  • William Duckworth
  • Michele Zito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4708)


We present algorithmic lower bounds on the size s d of the largest independent sets of vertices in random d-regular graphs, for each fixed d ≥ 3. For instance, for d = 3 we prove that, for graphs on n vertices, s d  ≥ 0.43475 n with probability approaching one as n tends to infinity.


Random Graph Minimum Degree Random Regular Graph Small Positive Real Number Mathematical Science Institute 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • William Duckworth
    • 1
  • Michele Zito
    • 2
  1. 1.Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200Australia
  2. 2.Department of Computer Science, University of Liverpool, Liverpool L69 3BXUK

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