5 problems

A weakly separating path system of a graph is a family of paths that weakly separates its edge set. Motivated by a question of Katona, Falgas-Ravry, Kittipassorn, Korandi, Letzter…

Let $G$ be an $n$-vertex graph, and let $\mathrm{ssp}(G)$ denote the minimum size of a strongly separating path system of $G$. Balogh–Csaba–Martin–Pluhár's conjecture. They conject…

Let $f:\binom{[n]}{2}\to [n]$ be the unique résumé of a diameter-$2$ path system $\mathcal{P}$. The system $\mathcal{P}$ is monotone if $f(i,j)\le f(i,k)$ whenever…

Let $G$ be a graph. A path system of $G$ is a set of paths in $G$. It is weakly separating if for every pair of edges of $G$ there exists a path in the system that contains exactly…

Asymptotic existence conjecture. Asymptotically almost every graph has an irreducible non-metrizable path system; specifically, this holds with probability