The Hadwiger number (G) of a graph G is the largest integer h such that the complete graph on h nodes Kh is a minor of G. Equivalently, (G) is the largest integer such that any graph on at most (G) nodes is a minor of G. The Hadwiger’s conjecture states that for any graph G, (G) (G), where (G) is the chromatic number of G. It is well-known that for any connected undirected graph G, there exists a unique prime factorization with respect to Cartesian graph products. If the unique prime… CONTINUE READING