An Equivalent Condition for the Reducibilty of Tropical Curves

In response to a recent algorithm for counting the number of isomorphism classes of irreducible tropical curves through 3d+g-1 general points in the plane satisfying certain psi-class conditions by Hannah Markwig and Johannes Rau in [MR08], a method for determining the reducibility of a tropical cruve in terms of it’s dual Newton polytope is required. This paper provides a solution by giving an equivalent condition for reducibility in terms of a mixed subdivision of the dual Newton polytope.