Stable Set Of Size Research Articles

On a list-coloring problem

We study the function f( G) defined for a graph G as the smallest integer k such that the join of G with a stable set of size k is not | V( G)|-choosable. This function was introduced recently in order to describe extremal graphs for a list-coloring version of a famous inequality due to Nordhaus and Gaddum (Dantas et al., Research Report 18, Laboratoire Leibniz-IMAG, Grenoble, 2000). Some bounds and some exact values for f( G) are determined.

Bounded Stable Sets: Polytopes and Colorings

A k-stable set in a graph is a stable set of size at most k. We study the convex hull of the k-stable sets of a graph, aiming for a complete inequality description. We also consider colorings of weighted graphs by k-stable sets, aiming for a relation between the values of an optimal coloring and an optimal fractional coloring. Results for k=2 and k=3 as well as a number of general conjectures linking fractional and integral colorings are given.