Graphs of small dimensions

LetG=(V, E) be a graph withn vertices. The direct product dimension pdim (G) (c.f. [10], [12]) is the minimum numbert such thatG can be embedded into a product oft copies of complete graphsK_n.In [10], Lovász, Neetil and Pultr determined the direct product dimension of matchings and paths and gave sharp bounds for the product dimension of cycles, all logarithmic in the number of vertices.