In this paper we give a simple polynomial-time algorithm to exactly count the
number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The
problems of counting ETs are known to be #P-complete for general graphs
(Brightwell and Winkler, (Brightwell and Winkler, 2005). To date, no
polynomial-time algorithm for counting Euler tours of any class of graphs is
known except for the very special case of series-parallel graphs (which have
treewidth 2).Comment: 16 pages, draf