Abstract
In this paper, for any prime p ⩾ 11 , we consider C p -decompositions of K m × K n and K m * K ¯ n and also C p -factorizations of K m × K n , where × and * denote the tensor product and wreath product of graphs, respectively, ( K m * K ¯ n is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices). It has been proved that for m , n ⩾ 3 , C p -decomposes K m × K n if and only if (1) either m or n is odd and (2) p | mn ( m - 1 ) ( n - 1 ) . Further, it is shown that for m ⩾ 3 , C p -decomposes K m * K ¯ n if and only if (1) ( m - 1 ) n is even and (2) p | m ( m - 1 ) n 2 . Except possibly for some valid pairs of integers m and n , the necessary conditions for the existence of C p -factorization of K m × K n are proved to be sufficient.
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