The singing voice and melody are important characteristics of music signals. In this paper we describe a method for extracting the singing voice and corresponding melody from "real-world" polyphonic music. The proposed method is inspired by ideas from Computational Auditory Scene Analysis. We formulate singing voice tracking and formation as a graph partitioning problem and solve it using the normalized cut which is a global criterion for segmenting graphs that has been used in Computer Vision. Sinusoidal modeling is used as the underlying representation. A novel harmonicity cue which we term Harmonically Wrapped Peak Similarity (HWPS) is introduced. Experimental results supporting the use of this cue are presented. In addition we show results for automatic melody extraction using the proposed approach.