  We present a first algorithm for finding Euler tours in undirected graphs in
the StrSort model. This model is a relaxation of the semi streaming model. The
graph is given as a stream of its edges and can only be read sequentially, but
while doing a pass over the stream we are allowed to write out another stream
which will be the input for the next pass. In addition, items in the stream are
sorted between passes. This model was introduced by Aggarwal et al. in 2004.
Here we apply this model to the problem of finding an Euler tour in a graph (or
to decide that the graph does not admit an Euler tour). The algorithm works in
two steps. In the first step, a single pass is conducted while a linear (in the
number of vertices $n$) amount of RAM is required. In the second step,
$\mathcal O(\log(n))$ passes are conducted while only $\mathcal O(\log(n))$ RAM
is required.
  We use an alteration of the algorithm of Atallah and Vishkin from 1984 for
finding Euler tours in parallel. It finds a partition of edge-disjoint circuits
and arranges them in a tree expressing their connectivity. Then the circuits
are merged according to this tree. In order to minimize the needed amount of
RAM, we evade the need to store the entire tree and use techniques suggested by
Aggarwal et al. to exchange information concerning the merging of circuits.
