Time-lapse microscopy imaging has advanced rapidly in last few decades and is producing large volume of data in cell and developmental biology. This has increased the importance of automated analyses, which depend heavily on cell segmentation and tracking as these are the initial stages when computing most biologically important cell properties. In this paper, we propose a novel joint cell segmentation and tracking method for fluorescence microscopy sequences, which generates a large set of cell proposals, creates a graph representing different cell events and then iteratively finds the most probable path within this graph providing cell segmentations and tracks. We evaluate our method on three datasets from ISBI Cell Tracking Challenge and show that our greedy nonoptimal joint solution results in improved performance compared with state of the art methods.