A note on graph minors and strong products

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