Abstract
AbstractA 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.