  Given a set of $n$ points $P$ in the plane, each colored with one of the $t$
given colors, a color-spanning set $S\subset P$ is a subset of $t$ points with
distinct colors. The minimum diameter color-spanning set (MDCS) is a
color-spanning set whose diameter is minimum (among all color-spanning sets of
$P$). Somehow symmetrically, the largest closest pair color-spanning set
(LCPCS) is a color-spanning set whose closest pair is the largest (among all
color-spanning sets of $P$). Both MDCS and LCPCS have been shown to be
NP-complete, but whether they are fixed-parameter tractable (FPT) when $t$ is a
parameter is still open. Motivated by this question, we consider the FPT
tractability of some matching problems under this color-spanning model, where
$t=2k$ is the parameter. The problems are summarized as follows: (1) MinSum
Matching Color-Spanning Set, namely, computing a matching of $2k$ points with
distinct colors such that their total edge length is minimized; (2) MaxMin
Matching Color-Spanning Set, namely, computing a matching of $2k$ points with
distinct colors such that the minimum edge length is maximized; (3) MinMax
Matching Color-Spanning Set, namely, computing a matching of $2k$ points with
distinct colors such that the maximum edge length is minimized; and (4)
$k$-Multicolored Independent Matching, namely, computing a matching of $2k$
vertices in a graph such that the vertices of the edges in the matching do not
share common edges in the graph. We show that the first three problems are
polynomially solvable (hence in FPT), while problem (4) is W[1]-hard.
