Extensions of Fractional Precolorings show Discontinuous Behavior
Identifieur interne : 001F35 ( Main/Exploration ); précédent : 001F34; suivant : 001F36Extensions of Fractional Precolorings show Discontinuous Behavior
Auteurs : Jan Van Den Heuvel [Royaume-Uni] ; Daniel Král' [Royaume-Uni] ; Martin Kupec [République tchèque] ; Jean-Sébastien Sereni [France] ; Jan Volec [Royaume-Uni]Source :
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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∈{2}∪ [3,∞) and any d. We determine the exact values of ε for k∈ (2,3) if d=4, and k∈ [2.5,3) if d=6, and give upper bounds for k∈(2,3) if d=5,7, and k∈(2,2.5) if d=6. Surprisingly, ε viewed as a function of k is discontinuous for all those values of d.
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Affiliations:
- France, Royaume-Uni, République tchèque
- Grand Est, Lorraine (région)
- Metz, Nancy
- Université de Lorraine
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type="acronym">DIMAP</orgName><desc><address><addrLine>University of Warwick Coventry CV4 7AL United Kingdom</addrLine><country key="GB"></country></address></desc><listRelation><relation active="#struct-302824" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-302824" type="direct"><org type="institution" xml:id="struct-302824" status="VALID"><orgName>University of Warwick [Coventry]</orgName><desc><address><addrLine>Coventry CV4 7AL</addrLine><country key="GB"></country></address><ref type="url">http://www2.warwick.ac.uk/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>Royaume-Uni</country></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>extension</term><term>fractional coloring</term><term>pre-coloring</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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∈{2}∪ [3,∞) and any d. We determine the exact values of ε for k∈ (2,3) if d=4, and k∈ [2.5,3) if d=6, and give upper bounds for k∈(2,3) if d=5,7, and k∈(2,2.5) if d=6. Surprisingly, ε viewed as a function of k is discontinuous for all those values of d.</div></front></TEI><affiliations><list><country><li>France</li><li>Royaume-Uni</li><li>République tchèque</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Lorraine</li></orgName></list><tree><country name="Royaume-Uni"><noRegion><name sortKey="Van Den Heuvel, Jan" sort="Van Den Heuvel, Jan" uniqKey="Van Den Heuvel J" first="Jan" last="Van Den Heuvel">Jan Van Den Heuvel</name></noRegion><name sortKey="Kral, Daniel" sort="Kral, Daniel" uniqKey="Kral D" first="Daniel" last="Král'">Daniel Král'</name><name sortKey="Volec, Jan" sort="Volec, Jan" uniqKey="Volec J" first="Jan" last="Volec">Jan Volec</name></country><country name="République tchèque"><noRegion><name sortKey="Kupec, Martin" sort="Kupec, Martin" uniqKey="Kupec M" first="Martin" last="Kupec">Martin Kupec</name></noRegion></country><country name="France"><region name="Grand Est"><name sortKey="Sereni, Jean Sebastien" sort="Sereni, Jean Sebastien" uniqKey="Sereni J" first="Jean-Sébastien" last="Sereni">Jean-Sébastien Sereni</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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