Extensions of Fractional Precolorings Show Discontinuous Behavior

HEUVEL, van den; Daniel KRÁĽ; M KUPEC; JS SERENI a J VOLEC. Extensions of Fractional Precolorings Show Discontinuous Behavior. Journal of Graph Theory. HOBOKEN: Wiley, 2014, roč. 77, č. 4, s. 299-329. ISSN 0364-9024. Dostupné z: https://doi.org/10.1002/jgt.21787.

Základní údaje

Originální název

Extensions of Fractional Precolorings Show Discontinuous Behavior

Autoři

HEUVEL, van den; Daniel KRÁĽ; M KUPEC; JS SERENI a J VOLEC

Vydání

Journal of Graph Theory, HOBOKEN, Wiley, 2014, 0364-9024

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Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.629

Označené pro přenos do RIV

Ne

DOI

https://doi.org/10.1002/jgt.21787

UT WoS

000343800600004

Klíčová slova anglicky

fractional coloring; precoloring extension

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Anotace

V originále

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.