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DOI : 10.1002/jgt.20335

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Journal of Graph Theory 59, 3 (2008) 229--238

List colorings with measurable sets

Jan Hladky 1, Daniel Král' 2, Jean-Sébastien Sereni 3, 4, Michael Stiebitz 5

(11/2008)

The measurable list chromatic number of a graph G is the smallest number such that if each vertex v of G is assigned a set L(v) of measure in a fixed atomless measure space, then there exist sets such that each c(v) has measure one and for every pair of adjacent vertices v and v'. We provide a simpler proof of a measurable generalization of Hall's theorem due to Hilton and Johnson [J Graph Theory 54 (2007), 179-193] and show that the measurable list chromatic number of a finite graph G is equal to its fractional chromatic number.

1 :	Centre for Discrete Mathematics and its Applications [Warwick] (DIMAP)
	University of Warwick
2 :	Institut teoretické informatiky (ITI)
	Charles University
3 :	Department of Applied Mathematics (KAM) (KAM)
	Univerzita Karlova v Praze
4 :	Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
	CNRS : UMR7089 – Université Paris VII - Paris Diderot
5 :	Institute of Mathematics - Technical university of Ilmenau (TU)
	Technische Universität Ilmenau

Domaine

:

Informatique/Mathématique discrète

Mots Clés : fractional chromatic number – Hall's theorem – list coloring – measurable sets

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Contributeur : Jean-Sébastien Sereni <>

Soumis le : Vendredi 28 Mai 2010, 15:22:16

Dernière modification le : Vendredi 28 Mai 2010, 17:05:05