Irreducible nonmetrizable path systems in graphs
Daniel Cizma, Nati Linial · Journal of Graph Theory · 2022
Abstract A path system in a graph is a collection of paths with a unique path for every two vertices . We say that is consistent if for any path , every subpath of is also in . It is metrizable if there exists a positive weight function such that is comprised of ‐shortest paths. We call irreducible if there does not exist a partition such that restricts to a path system on both and . In this paper, we construct an infinite family of nonmetrizable irreducible consistent path systems on certain Paley graphs.