van den Heuvel, Jan, Král', Daniel, Kupec, Martin, Sereni, Jean-Sébastien and Volec, Jan (2014) Extensions of fractional precolorings show discontinuous behavior. Journal of Graph Theory, 77 (4). pp. 299-329. ISSN 0364-9024
Abstract
We study the following problem: given a real number k and an integer d, what is the smallest ε such that any fractional ( k + ε ) -precoloring of vertices at pairwise distances at least d of a fractionally k-colorable graph can be extended to a fractional ( k + ε ) -coloring of the whole graph? The exact values of ε were known for k ϵ {2} ᴜ [3,∞] and any d. We determine the exact values of ε for k ϵ (2,3) if d = 4, and k ϵ [2.5,3) if d = 6, and give upper bounds for k ϵ (2,3) if d = 5,7, and k ϵ (2,2.5) if d = 6. Surprisingly, ε viewed as a function of k is discontinuous for all those values of d.
| Item Type: | Article |
|---|---|
| Official URL: | http://onlinelibrary.wiley.com/journal/10.1002/%28... |
| Additional Information: | © 2014 Wiley Periodicals, Inc. |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Date Deposited: | 28 Feb 2014 11:25 |
| URL: | http://eprints.lse.ac.uk/55918/ |
Actions (login required)
 |
Record administration - authorised staff only |
