ALCOMFT-TR-03-43

J. D\'\iaz, N. Do, M. Serna and N. Wormald
Bounds on the max and min bisection of random cubic and random 4-regular graphs
Barcelona. Work packages 2 and 4. September 2003.

Abstract: In this paper we present a randomized algorithm to compute the bisection width of cubic and 4-regular graphs. The analysis of the proposed algorithms on random graphs provides asymptotic upper bounds for the bisection width of random cubic and random 4-regular graphs with n vertices, giving upper bounds of 0.174039n for random cubic, and of 0.333333 n for random 4-regular. We also obtain asymptotic lower bounds for the size of the maximum bisection, for random cubic and random 4-regular graphs with n vertices, of 1.32697 n and 1.66667n, respectively. The randomized algorithms are derived from initial greedy algorithm and their analysis is based on the differential equation method.

Postscript file: ALCOMFT-TR-03-43.ps.gz (112 kb).