Treewidth is a lower bound on graph gonality

J van Dobben de Bruyn, D.C. Gijswijt

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
52 Downloads (Pure)

Abstract

We prove that the (divisorial) gonality of a finite connected graph is lower bounded by its treewidth. Graphs for which equality holds include the grid graphs and the complete multipartite graphs. We prove that the treewidth lower bound also holds for metric graphs (tropical curves) by constructing for any positive rank divisor on a metric graph a positive rank divisor of the same degree on a subdivision of the underlying combinatorial graph. Finally, we show that the treewidth lower bound also holds for a related notion of gonality defined by Caporaso and for stable gonality as introduced by Cornelissen et al.

Original languageEnglish
Pages (from-to)941-953
Number of pages13
JournalAlgebraic Combinatorics
Volume3
Issue number4
DOIs
Publication statusPublished - 2020

Keywords

  • Gonality
  • Metric graph
  • Treewidth
  • Tropical curve

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