ALCOMFT-TR-03-44

J. D\' \iaz, M. Serna and N. Wormald
Computation of the bisection width for random d-regular graphs
Barcelona. Work packages 2 and 4. September 2003.

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. We provide the bounds for 5<= d<= 12. The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to find bisections of d-regular graphs. We also give empirical values of the size of bisection found by the algorithm for some small values of d and compare it with numerical approximations of our theoretical bounds. Our analysis also gives asymptotic lower bounds for the size of the maximum bisection.

Postscript file: ALCOMFT-TR-03-44.ps.gz (91 kb).