Graph products and monochromatic multiplicities

Arcane two-edge-colourings of complete graphs were described in [13], in which there are significantly fewer monochromaticK_r's than in a random colouring (so disproving a conjecture of Erds [2]). Jagger, ovíek and Thomason [7] showed that the same colourings have fewer monochromaticG's than do random colourings for any graphG containingK₄.The purpose of this note is to point out that these colourings are not as obscure as might appear. There is in fact a large, natural and easily described class of colourings of the above kind; the specific examples used in [13] and [7] fall into this class.