Extensions of Fractional Precolorings Show Discontinuous Behavior
Jan van den Heuvel, Daniel Král͏̌, Martin Kupec, Jean‐Sébastien Sereni, Jan Volec · Journal of Graph Theory · 2014
Abstract We study the following problem: given a real number k and an integer d, what is the smallest ε such that any fractional ‐precoloring of vertices at pairwise distances at least d of a fractionally k‐colorable graph can be extended to a fractional ‐coloring of the whole graph? The exact values of ε were known for and any d. We determine the exact values of ε for if , and if , and give upper bounds for if , and if . Surprisingly, ε viewed as a function of k is discontinuous for all those values of d.