A non-degenerate rectangular subdivision is a subdivision of a rectangle into a set of non-overlapping rectangles S, such that no four rectangles meet in a point. We consider a problem that Katz and colleagues call strong polychromatic four-colouring: colouring the vertices of the subdivision with four colours, such that each rectangle of S has all colours among its four corners. By considering the possible colouring patterns, we can give short proofs of colourability for subdivisions that are sliceable or one-sided. We also present techniques and observations for non-sliceable, two-sided subdivisions, for which the colourability question is still open.
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