Summary: A \((G,H)\)-multidecomposition of \(K_m(\lambda)\) is the partition of \(K_m(\lambda)\) into edge disjoint copies of \(G\) and \(H\) with at least one copy of \(G\) and \(H\). The study of \((G,H)\)-multidecomposition has been introduced by A. A. Abueida and M. Daven [Graphs Comb. 19, No. 4, 433–447 (2003; Zbl 1032.05105)] and they raised the following conjecture: “For a integer \(m\geq n\geq 3\), there is a \((G_n,H_n)\)-multidecomposition of \(K_m(\lambda)\), where \((G_n,H_n)= (K_{1,n-1}, C_n)\)”.
In this paper we answer the analagous conjecture for \(K_{m,m}(\lambda)\) when

(i)

\((G_m,H_m)= (K_{1,m-1}, P)_m)\);

(ii)

\((G_m, H_m)= (C_m, K_{1,m-1})\) and

(iii)

\((G_m,H_m)= (C_m,P_m)\).