Bounds on the bisection width for random d -regular graphs

J. Díaz, M. J. Serna, N. C. Wormald

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20 Citations (Scopus)

Abstract

In this paper we provide an explicit way to compute asymptotically almost sure upper bounds on the bisection width of random d-regular graphs, for any value of d. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We provide bounds for 5 ≤ d ≤ 12. We also give empirical values of the size of the bisection found by the algorithm for some small values of d and compare them with numerical approximations of our theoretical bounds. Our analysis also gives asymptotic lower bounds for the size of the maximum bisection.

Original languageEnglish
Pages (from-to)120-130
Number of pages11
JournalTheoretical Computer Science
Volume382
Issue number2
DOIs
Publication statusPublished - 31 Aug 2007
Externally publishedYes

Keywords

  • Bisection width
  • Random regular graphs

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