The aim of this paper is to describe, for a given graphical partition λ of weight 2m and rank r, the set of all maximal graphical partitions μ of weight 2m that dominate λ. To do this, it is enough to find the set of heads of such partitions. Theorem 1 states that, for any natural number t, the set of heads of all maximal graphical partitions μ of weight 2m and rank t dominating λ forms an interval of the integer partition lattice if such partitions μ of rank t exist. Algorithms are also provided for finding the smallest and largest elements of this interval.