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 it with numerical approximations of our theoretical bounds. Our analysis also gives asymptotic lower bounds for the size of the maximum bisection.
Diaz et al. REF provide almost sure upper bounds for the bisection width of randomly generated regular graphs.
Bounds on the bisection width for random d -regular graphs
Theor. Comput. Sci.
Theor. Comput. Sci.
Mathematics Computer Science