3 problems

Let $k$ and $\lambda$ be fixed positive integers with $k\geqslant \lambda+1$. Let $(X,\mathcal B)$ be a cyclic $(v,k,\lambda)$-BIBD with $v\geqslant v_0$, where $v_0$ is an integer…

Let $(V,\mathcal{B})$ be a cyclic $(v,k,1)$-design: the blocks are partitioned into orbits under a cyclic automorphism, and a base block is one chosen block from each orbit. Disjoi…

Let $T$ be a tree with $n+1$ vertices, and identify the vertices of $K_{2n+1}$ with the integers modulo $2n+1$. A cyclic decomposition into copies of $T$ consists of the cyclic shi…