On the length of the shortest path in a sparse Barak-Erdős graph

Bastien Mallein, Pavel Tesemnikov

We consider an inhomogeneous version of the Barak-Erdős graph, i.e. a directed Erős-Rényi random graph on $\{1,\dots ,n\}$ with no loop. Given $f$ a Riemann-integrable non-negative…