Bounds on the max and min bisection of random cubic and random 4-regular graphs

Authors:
J. Díaz;N. Do;M. J. Serna;N. C. Wormald
Affiliations:
Department de Llenguatges i Sistemes, Universitat Politecnica de Catalunya, Jordi Girona Salgado 1-3, Barcelona 08034, Spain;Department of Mathematics and Statistics, University of Melbourne, Melborne, Vic. 3010, Australia;Department de Llenguatges i Sistemes, Universitat Politecnica de Catalunya, Jordi Girona Salgado 1-3, Barcelona 08034, Spain;Department of Mathematics and Statistics, University of Melbourne, Melborne, Vic. 3010, Australia
Venue:
Theoretical Computer Science - Selected papers in honor of Lawrence Harper
Year:
2003

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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 0.333333n 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 1.32697n and 1.66667n, respectively. The randomized algorithms are derived from initial greedy algorithm and their analysis is based on the differential equation method.