On the Hadwiger's conjecture for graph products (Q864168)

The Hadwiger's conjecture for graphs is given in terms of their prime factorization. It is shown (among other things) that the Hadwiger conjecture is true for a graph \(G\) if the product dimension of \(G\) is at least \(2\log_2(\chi(G))+ 3\). The Hadwiger number of well-known graph products like \(d\)-dimensional hypercubes, Hamming graphs and the \(d\)-dimensional grids are consider, too.