Superconcentrators of Density 25.3
  An $N$-superconcentrator is a directed, acyclic graph with $N$ input nodes and $N$ output nodes such that every subset of the inputs and every subset of the outputs of same cardinality can be connected by node-disjoint paths. It is known that linear-size and bounded-degree superconcentrators exist. We prove the existence of such superconcentrators with asymptotic density $25.3$ (where the density is the number of edges divided by $N$). The previously best known densities were $28$ \cite{Scho2006} and $27.4136$ \cite{YuanK12}. 
Vladimir Kolmogorov and Michal Rolinek
cs.DM math.CO