Characterization of Line Arrangement for which the Fundamental Group of   the Complement is a Direct Product of Free Groups
  Kwai Man Fan proved that if the intersection lattice of a line arrangement does not contain a cycle, then the fundamental group of its complement is a direct sum of infinite and cyclic free groups. He also conjectured that the converse is true as well. The main purpose of this paper is to prove this conjecture 
Eliyahu Meital, Liberman Eran, Schaps Mary, Teicher Mina