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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.313
URN: urn:nbn:de:0030-drops-47057
URL: http://drops.dagstuhl.de/opus/volltexte/2014/4705/
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Kwok, Tsz Chiu ; Lau, Lap Chi

Lower Bounds on Expansions of Graph Powers

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Abstract

Given a lazy regular graph G, we prove that the expansion of G^t is at least sqrt(t) times the expansion of G. This bound is tight and can be generalized to small set expansion. We show some applications of this result.

BibTeX - Entry

@InProceedings{kwok_et_al:LIPIcs:2014:4705,
  author =	{Tsz Chiu Kwok and Lap Chi Lau},
  title =	{{Lower Bounds on Expansions of Graph Powers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
  pages =	{313--324},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-74-3},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{28},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4705},
  URN =		{urn:nbn:de:0030-drops-47057},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2014.313},
  annote =	{Keywords: Conductance, Expansion, Graph power, Random walk}
}

Keywords: Conductance, Expansion, Graph power, Random walk
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)
Issue Date: 2014
Date of publication: 02.09.2014


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