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Exact counting of Euler Tours for Graphs of Bounded Treewidth (1310.0185v1)
Published 1 Oct 2013 in cs.DM and math.CO
Abstract: 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).