Coloring Superstable Graphs
Given a graph G=(V,E), a coloring of G in \kappa colors is a map c:V\to \kappa in which adjacent vertices are colored in different colors. The chromatic number of G is the smallest such \kappa.
We will briefly review some questions and conjectures on the chromatic number of infinite graphs and will mainly concentrate on the following strong form of Taylor's conjecture:
If G is an infinite graph with chromatic number\geq \alepha_1 then it contains all finite subgraphs of Sh_n(\omega) for some n, where Sh_n(\omega) is the n-shift graph (which we will introduce).
Joint work with Itay Kaplan and Saharon Shelah.