Catalan-many tropical morphisms to trees; Part I: Constructions

30 Jul 2020 Draisma Jan Vargas Alejandro

We investigate the tree gonality of a genus-$g$ metric graph, defined as the minimum degree of a tropical morphism from any tropical modification of the metric graph to a metric tree. We give a combinatorial constructive proof that this number is at most $\lceil g/2 \rceil + 1$, a fact whose proofs so far required an algebro-geometric detour via special divisors on curves... (read more)

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