Publication details
Extensions of Fractional Precolorings Show Discontinuous Behavior
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Graph Theory |
| Citation | |
| Doi | http://dx.doi.org/10.1002/jgt.21787 |
| Keywords | fractional coloring; precoloring extension |
| Description | We study the following problem: given a real number k and an integer d, what is the smallest e 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 is an element of {2} boolean OR [3,infinity) and any d. We determine the exact values of epsilon for k is an element of (2, 3) if d = 4, and k is an element of [2.5, 3) if d = 6, and give upper bounds for k is an element of (2, 3) if d = 5, 7, and k is an element of (2, 2.5) if d = 6. Surprisingly, epsilon viewed as a function of k is discontinuous for all those values of d. (C) 2014 Wiley Periodicals, Inc. |