Date:

Wed, 29/01/202009:45-11:45

Location:

Ross building - Room 63

**Yatir Halevi**will speal about

**Coloring Stable Graphs**.

Title: Coloring Stable Graphs

__Abstract:__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 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).

The conjecture was disproved by Hajnal-Komjath.

However, we will present an elementary proof for \omega-stable graphs

and if time permits will discuss stable graphs in general.

Joint work with Itay Kaplan, Saharon Shelah (and parts with Elad Levi)