Balanced Quatrefoil Decomposition of Complete Multigraphs SUMMARY We

show that the necessary and sufficient condition for the existence of a balanced quatrefoil decomposition of the complete multigraph λKn is n ≥ 9andλ(n − 1) ≡ 0 (mod 24). Decomposition algorithms are also given. key words: balanced quatrefoil decomposition, complete multigraph 1