Let Cn and Sn respectively denote a cycle and star with n edges. Let Kn denote a complete graph on n vertices. In this paper, it is shown that for any non-negative integers α and β and any positive integer n ≥ 6, there exists a decomposition of Kn into α copies of C6 and β copies of S3 if and only if 6α + 3β = n(n − 1) 2 β ≠ 1, 2 when n is odd, and β ≥ ⌈n/4⌉ when n is even.
Lakshmanan et al. (Wed,) studied this question.