Irreducible nonmetrizable path systems in graphs

Daniel Cizma; Nati Linial

doi:10.1002/jgt.22854

Irreducible nonmetrizable path systems in graphs

Daniel Cizma^*, Nati Linial

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English
Pages (from-to)	5-14
Number of pages	10
Journal	Journal of Graph Theory
Volume	102
Issue number	1
DOIs	https://doi.org/10.1002/jgt.22854
State	Published - Jan 2023

Bibliographical note

Funding Information:
Open access publishing facilitated by MALMAD hybrid - Hebrew University of Jerusalem.

Publisher Copyright:
© 2022 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.

Keywords

Paley graphs
irreducibility
metrizability
path systems

Access to Document

10.1002/jgt.22854

Cite this

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Irreducible nonmetrizable path systems in graphs

Abstract

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Keywords

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