  We introduce the notion of a conjugation-free geometric presentation for a
fundamental group of a line arrangement's complement, and we show that the
fundamental groups of the following family of arrangements have a
conjugation-free geometric presentation: A real arrangement L, whose graph of
multiple points is a union of disjoint cycles, has no line with more than two
multiple points, and where the multiplicities of the multiple points are
arbitrary.
  We also compute the exact group structure (by means of a semi-direct product
of groups) of the arrangement of 6 lines whose graph consists of a cycle of
length 3, and all the multiple points have multiplicity 3.
