ABSTRACT. In the first part of this paper, we discuss the notion of irreducibility of cycles in the moduli spaces of n-marked rational tropical curves. We prove that Psi-classes and vital divisors are irreducible, and that locally irreducible divisors are also globally irreducible for n ≤ 6. In the second part of the paper, we show that the locus of point configurations in (R 2) n in special position for counting rational plane curves (defined in two different ways) can be given the structure a tropical cycle of codimension 1. In addition, we compute explicitly the weights of this cycle. 1
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