Discrete and metric divisorial gonality can be different

Josse van Dobben de Bruyn*, Harry Smit, Marieke van der Wegen

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

This paper compares the divisorial gonality of a finite graph G to the divisorial gonality of the associated metric graph Γ(G,1) with unit lengths. We show that dgon(Γ(G,1)) is equal to the minimal divisorial gonality of all regular subdivisions of G, and we provide a class of graphs for which this number is strictly smaller than the divisorial gonality of G. This settles a conjecture of M. Baker [3, Conjecture 3.14] in the negative.

Original languageEnglish
Article number105619
Pages (from-to)1-19
JournalJournal of Combinatorial Theory. Series A
Volume189
DOIs
Publication statusPublished - Jul 2022

Keywords

  • Chip-firing game
  • Finite graph
  • Gonality
  • Metric graph

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