  Given a set $P$ of $n$ points in $R^{d}$, a tour is a closed simple path that
covers all the given points, i.e. a Hamiltonian cycle. % In $P$ if no three
points are collinear then the points are said to be in general position. A
\textit{link} is a line segment connecting two points and a rectilinear link is
parallel to one of the axes. The problems of defining a path and a tour with
minimum number of links, also known as Minimum-Link Covering Path and
Minimum-Link Covering Tour respectively are proven to be NP-hard in $R^2$. The
corresponding rectilinear versions are also NP-hard in $R^2$.
  A set of points is said to be in \textit{general position} for rectilinear
versions of the problems if no two points share any coordinate. We call a set
of points in $R^{d}$ to be in \textit{relaxed general position} if no three
points share any coordinate and any two points can share at most one
coordinate. That is, if the points are either in general position or in relaxed
general position then an axis parallel line can contain at most one point. If
points are in relaxed general position then these problems are NP-hard in
$R^{10}$. We prove that these two problems are in fact NP-hard in $R^{4}$. If
points in $R^{d},~d>1$ are in general position then the time complexities of
these problems, both basic and rectilinear versions, are unknown.
