Graph matching is one of the principal methods to formulate the correspondence between two set of points in computer vision and pattern recognition. Most formulations are based on the minimization of a difficult energy function which is known to be NP-hard. Traditional methods solve the minimization problem approximately. In this paper, we derive an exact minimization algorithm and successfully applied to action recognition in videos. In this context, we take advantage of special properties of the time domain, in particular causality and the linear order of time, and propose a new spatio-temporal graphical structure. We show that a better solution can be obtained by exactly solving an approximated problem instead of approximately solving the original problem.