Summary: Let \(G\) be a connected graph with maximum degree \(k\) (other than a complete graph or odd cycle), let \(W\) be a precolored set of vertices in \(G\) inducing a subgraph \(F\), and let \(D\) be the minimum distance in \(G\) between components of \(F\). If the components of \(F\) are complete graphs and \(D\geq 8\) (for \(k\geq 4\)) or \(D\geq 10\) (for \(k = 3\)), then every proper \(k\)-coloring of \(F\) extends to a proper \(k\)-coloring of \(G\). If the components of \(F\) are single vertices and \(D\geq 8\), and the vertices outside \(W\) are assigned color lists of size \(k\), then every \(k\)-coloring of \(F\) extends to a proper coloring of \(G\) with the color on each vertex chosen from its list. These results are sharp.