Extending Fractional Precolorings
Daniel Král͏̌, Matjaž Krnc, Martin Kupec, Borut Lužar, Jan Volec · SIAM Journal on Discrete Mathematics · 2012
For every $d\ge 3$ and $k\in\{2\}\cup[3,\infty)$, we determine the smallest $\varepsilon$ such that every fractional $(k+\varepsilon)$-precoloring of vertices at mutual distance at least d of a graph G with fractional chromatic number equal to k can be extended to a proper fractional $(k+\varepsilon)$-coloring of G. Our work complements analogous results of Albertson for ordinary colorings and those of Albertson and West for circular colorings.