Uncover low degree vertices and minimise the mess: independent sets in random regular graphs

Authors:
William Duckworth;Michele Zito
Affiliations:
Mathematical Sciences Institute, Australian National University, Canberra, Australia;Department of Computer Science and University of Liverpool, Liverpool, UK
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

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Abstract

We present algorithmic lower bounds on the size sd 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, sd ≥ 0.43475n with probability approaching one as n tends to infinity.