Christian Rubio:
On m-factorizations of complete multigraphs and finite projective spaces
The complete multigraph $\lambda K_{v}$ has v vertices and $\lambda$ edges joining each pair of vertices.
An m-factor of the complete multigraph $\lambda K_{v}$ is a set of pairwise vertex-disjoint m-regular subgraphs,
such that these subgraphs induce a partition of the vertices.
An m-factorization of $\lambda K_{v}$ is a set of pairwise edge-disjoint m-factors
such that these m-factors induce a partition of the edges.
If the m-factors are pairwise distinct, then it is called simple.
Furthermore, an m-factorization of $\lambda K_{v}$ is decomposable
if there exist positive integers $\lambda_{1}$ and $\lambda_{2}$ such that
$\lambda_{1}+\lambda_{2}=\lambda$ and $\lambda K_{v}$ is the union of the m-factorizations
$\lambda_{1}K_{v}$ and $\lambda_{2}K_{v}$,
otherwise it is called indecomposable.
In this talk we will discuss simple and indecomposable m-factorizations of $\lambda K_v$
related to finite projective spaces for different values of m, $\lambda$ and v.