\title {Irreducible cycles and points in special position in moduli spaces for 
  tropical curves}
\author{Andreas Gathmann \\
  \small Fachbereich Mathematik \\[-0.8ex]
  \small TU Kaiserslautern \\[-0.8ex]
  \small Postfach 3049, 67653 Kaiserslautern, Germany \\
  \small\tt andreas@mathematik.uni-kl.de \\
\and
  Franziska Schroeter \\
  \small Cluster of Excellence for Computer Science \\[-0.8ex]
  \small Universit\"at des Saarlandes \\[-0.8ex]
  \small Postfach 151150, 66041 Saarbr\"ucken, Germany \\
  \small\tt schroeter@math.uni-sb.de
}

\date{\dateline{Dec 8, 2011}{Oct 31, 2012}\\
\small Mathematics Subject Classifications: 14N10, 14T05}

\maketitle

\begin {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 \le 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.
\end {abstract}

