In a connected simple graph \( G = (V(G),E(G)) \) , each vertex is assigned one of \( c \) colors, where \( V(G) = \bigcup _{\ell =1}^{c} V_{\ell } \) and \( V_{\ell } \) denotes the set of vertices of color \(\ell \) . A subset \( S \subseteq V(G) \) is called a selective subset if, for every \( \ell \) , \( 1 \le \ell \le c \) , every vertex \( v \in V_{\ell } \) has at least one nearest neighbor in \( S \cup (V(G) \setminus V_{\ell }) \) that also lies in \( V_{\ell } \) . The Minimum Selective Subset (MSS) problem asks for a selective subset of minimum size. We show that the MSS problem is log-APX-hard on general graphs, even when \( c = 2 \) . As a consequence, the problem does not admit a polynomial-time approximation scheme (PTAS) unless \(\textsf {P} = \textsf {NP} \) . On the positive side, we present a PTAS for unit disk graphs that does not require a geometric representation and applies for arbitrary c. We further prove that MSS remains NP-complete in unit disk graphs for arbitrary \(c\) . In addition, we show that the MSS problem is APX-hard on circle graphs, even when \(c=2\) . The full version of this work can be found in [1].