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For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1 $w_{4}^{1} = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.

A model theory approach to structural limits

Jaroslav Nešetřil, Patrice Ossona de Mendez (2012)

Commentationes Mathematicae Universitatis Carolinae

The goal of this paper is to unify two lines in a particular area of graph limits. First, we generalize and provide unified treatment of various graph limit concepts by means of a combination of model theory and analysis. Then, as an example, we generalize limits of bounded degree graphs from subgraph testing to finite model testing.

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A metric graph satisfying [...] w 4 1 = 1 $w_{4}^{1} = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $dim (W_{4}^{1}) = 1$

A model theory approach to structural limits

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