Bisecting sparse random graphs

Malwina J. Luczak, Colin McDiarmid
2000 Random structures & algorithms (Print)  
Consider partitions of the vertex set of a graph G into two sets with sizes differing by at most 1: the bisection width of G is the minimum over all such partitions of the number of "cross edges" between the parts. We are interested in sparse random graphs Ž . G with edge probability crn. We show that, if c ) ln 4, then the bisection width is ⍀ n n, c r n with high probability; while if cln 4, then it is equal to 0 with high probability. There are corresponding threshold results for partitioning into any fixed number of parts.
doi:10.1002/1098-2418(200101)18:1<31::aid-rsa3>;2-1 fatcat:fcixvpt7dbembkapxlcdd2smbi