  Dissections of a square into smaller squares, with the smaller squares having
relatively prime sizes, are known as Mrs Perkins's quilts. A representation of
these dissections using graphs is presented. The edges are directed and
coloured North-South or West-East, and the graph corresponds naturally to the
dissection. This representation allowed the exhaustive generation of all
dissections up to order 18, using the plantri software. The results were
cross-checked by generating all dissections of small sizes using a direct
approach. The results confirm, extend and introduce several integer sequences.
