Geodesic
Combinatorics of tropical Hurwitz cycles
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1027-1058.

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We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points, the resulting cycles are weakly irreducible, i.e. an integer multiple of an irreducible cycle. We study how Hurwitz cycles can be written as divisors of rational functions and show that they are numerically equivalent to a tropical version of a representation as a sum of boundary divisors. The results and counterexamples in this paper were obtained with the help of a-tint, an extension for polymake for tropical intersection theory.
Classification : 14T05
Keywords: double Hurwitz numbers, tropical Hurwitz cycle 
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     title = {Combinatorics of tropical {Hurwitz} cycles},
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Hampe, Simon. Combinatorics of tropical Hurwitz cycles. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 1027-1058. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a5/