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For 1 and n 1, we examine the simplicial complex of graphs on n vertices in which each vertex has degree at most ; we identify a given graph with its edge set and admit one loop at each vertex. = 1 yields the matching complex, and it is known that there is 3-torsion in degree d of the homology of this complex whenever n 4 3 d n 6 2 . We establish

3-torsion in the Homology of Complexes of Graphs of Bounded Degree