Tracking of cells in live-imaging microscopy videos of epithelial sheets is a powerful tool for investigating fundamental processes in embryonic development. Observing the growth, proliferation, intercalation, and apoptosis of individual cells helps us understand how global morphogenetic processes, such as tissue invagination or extension, are locally regulated and controlled. Accurate cell tracking requires correctly resolving cells moving in and out of field of view between frames, cell neighbour exchanges, cell removal and cell division events. Here, we present a novel algorithm for epithelial cell tracking. The algorithm exploits the graph-theoretic concept of a `maximum common subgraph' to track cells between successive frames of a video. It does not require the adjustment of tissue-specific parameters, and scales in polyonomial time with tissue size. The algorithm does not rely on precise positional information and thus permits large cell movements between frames, enabling cell tracking in data sets acquired at low temporal resolution due to experimental constraints such as photoxicity.