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Lower Bounds on Expansions of Graph Powers

Authors Tsz Chiu Kwok, Lap Chi Lau

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Tsz Chiu Kwok
Lap Chi Lau

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Tsz Chiu Kwok and Lap Chi Lau. Lower Bounds on Expansions of Graph Powers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 313-324, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


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.
  • Conductance
  • Expansion
  • Graph power
  • Random walk


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