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In this paper, we consider coloring of graphs under the assumption that somevertices are already colored. Let $G$ be an $r$-colorable graph and let$P\subset V(G)$. Albertson [J.\ Combin.\ Theory Ser. B \textbf{73} (1998),189--194] has proved that if every pair of vertices in $P$ have distance atleast four, then every $(r+1)$-coloring of $G[P]$ can be extended to an$(r+1)$-coloring of $G$, where $G[P]$ is the subgraph of $G$ induced by $P$. Inthis paper, we allow $P$ to have pairs of vertices of distance at most three,and investigate how the number of such pairs affects the number of colors weneed to extend the coloring of $G[P]$. We also study the effect of pairs ofvertices of distance at most two, and extend the result by Albertson and Moore[J.\ Combin.\ Theory Ser. B \textbf{77} (1999) 83--95].

Precoloring extension involving pairs of vertices of small distance