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{\bf Weiwen Gu}
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{\bf A Decomposition Algorithm for the Oriented Adjacency Graph of the Triangulations of a Bordered Surface with Marked Points}
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In this paper we consider an oriented version of adjacency graphs of
triangulations of bordered surfaces with marked points.
We develop an algorithm that determines whether a given oriented graph
is an oriented adjacency graph of a triangulation. If a given
oriented graph corresponds to many triangulations, our algorithm finds
all of them. As a corollary we find out that there are only finitely
many oriented connected graphs with non-unique associated
triangulations. We also discuss a new algorithm which determines
whether a given quiver is of finite mutation type. This algorithm is
linear in the number of nodes and is more effective than the
previously known one.
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