(3,4)-Cycle System of K_(m(n))

In 1981, Alspach conjectured that if 3 ≤ m_i ≤ v, v is odd and v(v - 1)/2 = m_1 + m_2 + ... + m_t, then the complete graph K_v can be decomposed into t cycles of lengths m_1, m_2,...,m_t, respectively; if v is even, v(v - 2)/2 = m_1 + m_2 + ... +m_t then the complete graph minus a one-factor K_v - F can be decomposed into t cycles of lengths m_1, m_2,...,m_t, respectively. In this paper, we extend the study to the decomposition of the complete m equipartite graph K_(m(n)). For m_i є {3,4}, we prove that the trivial necessary conditions are also sufficient when m ≡ 1 or 3 (mod 6).