Gregarious Kite Decomposition of Tensor Product of Complete Graphs

A kite decomposition of a multipartite graph is said to be gregarious if every kite in the decomposition has all its vertices in different partite sets. In this paper, we show that there exists a gregarious kite decomposition of Km×KnKm×Kn if and only if mn(m−1)(n−1)≡0(mod8), where × denotes the tensor product of graphs.