  We study a variant of the geometric multicut problem, where we are given a
set $\mathcal{P}$ of colored and pairwise interior-disjoint polygons in the
plane. The objective is to compute a set of simple closed polygon boundaries
(fences) that separate the polygons in such a way that any two polygons that
are enclosed by the same fence have the same color, and the total number of
links of all fences is minimized. We call this the minimum link fencing (MLF)
problem and consider the natural case of bounded minimum link fencing (BMLF),
where $\mathcal{P}$ contains a polygon $Q$ that is unbounded in all directions
and can be seen as an outer polygon. We show that BMLF is NP-hard in general
and that it is XP-time solvable when each fence contains at most two polygons
and the number of segments per fence is the parameter. Finally, we present an
$O(n \log n)$-time algorithm for the case that the convex hull of $\mathcal{P}
\setminus \{Q\}$ does not intersect $Q$.
