Counting cycles in labeled graphs: The nonpositive immersion property   for one-relator groups
  We prove a rank 1 version of the Hanna Neumann Theorem. This shows that every one-relator 2-complex without torsion has the nonpositive immersion property. The proof generalizes to staggered and reducible 2-complexes. 
Joseph Helfer, Daniel T. Wise
math.GR