Twisted conjugacy classes for polyfree groups
  Let $G$ be a finitely generated polyfree group. If $G$ has nonzero Euler characteristic then we show that $Aut(G)$ has a finite index subgroup in which every automorphism has infinite Reidemeister number. For certain $G$ of length 2, we show that the number of Reidemeister classes of every automorphism is infinite. 
Alexander Fel'shtyn, Daciberg Gon\c{c}alves and Peter Wong