Irreducible nonmetrizable path systems in graphs

Daniel Cizma, Nati Linial

Research output: Contribution to journalArticlepeer-review


A path system (Formula presented.) in a graph (Formula presented.) is a collection of paths with a unique (Formula presented.) path for every two vertices (Formula presented.). We say that (Formula presented.) is consistent if for any path (Formula presented.), every subpath of (Formula presented.) is also in (Formula presented.). It is metrizable if there exists a positive weight function (Formula presented.) such that (Formula presented.) is comprised of (Formula presented.) -shortest paths. We call (Formula presented.) irreducible if there does not exist a partition (Formula presented.) such that (Formula presented.) restricts to a path system on both (Formula presented.) and (Formula presented.). In this paper, we construct an infinite family of nonmetrizable irreducible consistent path systems on certain Paley graphs.

Original languageEnglish
Pages (from-to)5-14
Number of pages10
JournalJournal of Graph Theory
Issue number1
StatePublished - Jan 2023


  • irreducibility
  • metrizability
  • Paley graphs
  • path systems

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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