List colorings with measurable sets

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

1 DIMAP - Centre for Discrete Mathematics and its Applications [Warwick]
2 ITI - Institut teoretické informatiky
3 KAM - Department of Applied Mathematics (KAM)
4 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
5 Institute of Mathematics - Technical University of Ilmenau

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.

Mots clés: fractional chromatic number; Hall's theorem; list coloring; measurable sets

Domaines: Mathématique discrète [cs.DM]

Jan Hladky, Daniel Král', Jean-Sébastien Sereni, Michael Stiebitz. List colorings with measurable sets. Journal of Graph Theory, 2008, 59 (3), pp.229--238. ⟨10.1002/jgt.20335⟩. ⟨hal-00487293⟩