Unifying Maximum Cut and Minimum Cut of a Planar Graph

Absfmcf-We consider the real-weight maximum cut of a planar graph. Given an undirected planar graph with real-valued weights associated with its edges, find a partition of the vertices into two nonemply sets such that the sum of the weights of the edges connecting the two sets is maximum. The conventional maximum cut and minimum cut problems assume nonnegative edge weights, and thus are special cases of the real-weight maximum cut. We develop an O(n3I2 logn) algorithm for finding a real-weight maximum cut of a planar graph where n is the number of vertices in the graph. The best maximum cut algorithm previously known for planar graphs has the running time of O (n 3) .