$\lambda$-fold $K_{2,5}$-Designs

Abstract

In this note, we present necessary conditions for decomposing $\lambda K_n$ into copies of $K_{2,5}$, and show that these conditions are sufficient except for $\lambda =5$ and $n=8$, and possibly for the following cases: $\lambda =1$ and $n=40$; and $\lambda =3$ and $n=16$ or $20$.