  We study the following problem: given a real number k and integer d, what is
the smallest epsilon such that any fractional (k+epsilon)-precoloring of
vertices at pairwise distances at least d of a fractionally k-colorable graph
can be extended to a fractional (k+epsilon)-coloring of the whole graph? The
exact values of epsilon were known for k=2 and k\ge3 and any d. We determine
the exact values of epsilon for k \in (2,3) if d=4, and k \in [2.5,3) if d=6,
and give upper bounds for k \in (2,3) if d=5,7, and k \in (2,2.5) if d=6.
Surprisingly, epsilon viewed as a function of k is discontinuous for all those
values of d.
