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Extensions of fractional precolorings show discontinuous behavior

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, Online . ISSN 0364-9024 (In Press)

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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
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 28 Feb 2014 11:25
URL: http://eprints.lse.ac.uk/55918/

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