Relations among some fractional list coloring parameters and corresponding squishy-set coloring parameters
by
P.D. Johnson, Jr.
Auburn University
Coauthors: A.J.W.Hilton (University of Reading), T.Slivnik (Parts Unknown)

List coloring parameters arise from the problem of properly coloring the vertices of a graph with subsets of finite sets assigned to the vertices. Squishy-set coloring parameters arise from the problem of properly coloring the vertices of a graph with measurable subsets of measurable sets from an atomless positive measure space that have been assigned to the vertices. In this work the atomless positive measure space will be the real line with Lebesgue measure. We give some results and pose some problems on the relations between the squishy choice number and the fractional choice number (which is the same as the fractional chromatic number), between the squishy Hall number and the fractional Hall number, and between the squishy Hall-con dition number and the fractional Hall-condition number (also known as the Hall ratio).

Date received: April 19, 2001