List colorings with measurable sets

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 c(v) L(v) such that each c(v) has measure one and c(v)c(v ) = for every pair of adjacent vertices v and v . We show that the measurable list chromatic number of a finite graph G is equal to its fractional chromatic number. We also apply our method to obtain an alternative proof of a measurable generalization of Hall's theorem due to Hilton and Johnson [J. Graph Theory 54 (2007), 179

• Type: Journal
• Year: 2008
• Where: JGT
• Authors: Jan Hladký, Daniel Král, Jean-Sébastien Sereni, Michael Stiebitz
• Keywords: Fixed Atomless Measure, JGT 2008, List Chromatic Number, Measurable List