  Let G be a graph with a perfect matching. A complete forcing set of G is a
subset of edges of G to which the restriction of every perfect matching is a
forcing set of it. The complete forcing number of G is the minimum cardinality
of complete forcing sets of G. Xu et al. gave a characterization for a complete
forcing set and derived some explicit formulas for the complete forcing numbers
of cata-condensed hexagonal systems. In this paper, we consider general
hexagonal systems. We present an upper bound on the complete forcing numbers of
hexagonal systems in terms of elementary edge-cut cover and two lower bounds by
the number of hexagons and matching number respectively. As applications, we
obtain some explicit formulas for the complete forcing numbers of some types of
hexagonal systems including parallelogram, regular hexagon- and
rectangle-shaped hexagonal systems.
