A note on 3D orthogonal graph drawing

Some recent papers for three-dimensional orthogonal graph drawing use a technique introduced by Kolmogorov and Barzdin. This technique consists of assigning x-coordinates and y-coordinates, and then computing compatible z-coordinates, which was done via vertex-colouring a conflict graph. In this note, we show that compatible z-coordinates can also be found by edge-colouring a (different) conflict graph. As a consequence, the time complexity for computing the drawings decreases, and the volumes of the drawings are reduced as well.