Discrete and metric divisorial gonality can be different
Publication date
2022-07
Authors
van Dobben de Bruyn, Josse
Smit, Harry
van der Wegen, Marieke
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Advisors
Supervisors
Document Type
Article
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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.
Keywords
Chip-firing game, Finite graph, Gonality, Metric graph, Theoretical Computer Science, Discrete Mathematics and Combinatorics, Computational Theory and Mathematics
Citation
van Dobben de Bruyn, J, Smit, H & van der Wegen, M 2022, 'Discrete and metric divisorial gonality can be different', Journal of Combinatorial Theory. Series A, vol. 189, 105619, pp. 1-19. https://doi.org/10.1016/j.jcta.2022.105619