Decomposing Crowns into 4- and 8-cycles (Circuits)

In this paper, we investigate the problems of decomposing the crown C(subscript n, k) (resp. directed crown C(superscript * subscript n, k)) into 4-cycles and 8-cycles (resp. 4-circuits and 8-circuits). Some sufficient conditions of the problems are given. Moreover, we obtain the necessary and sufficient conditions of 4-circuit decompositions and 8-circuit decompositions of C(superscript * subscript n, n-1).