A note on graph minors and strong products

Let G⊠HG⊠H and G□HG□H denote the strong and Cartesian products of graphs GG and HH, respectively. In this note, we investigate the graph minor in products of graphs. In particular, we show that, for any simple connected graph GG, the graph G⊠K2G⊠K2 is a minor of the graph G□QrG□Qr by a construction method, where QrQr is an rr-cube and r=χ(G)r=χ(G). This generalizes an earlier result of Kotlov [2].