Title: On Shelah-Soifer Class of Graphs<br><br>



Abstract: The chromatic number of the graph G is the smallest number of
colors that are required to color the vertices of G so that no two 
adjacent vertices of G are of the same color.  A graph is said to have the
Shelah-Soifer property if its chromatic number varies depending on whether
we accept AC (Axiom of Choice) or not.  We will look at some examples of
Shelah-Soifer graphs. In addition we will  try to "understand" why such
graphs exists.  Some observations suggests that there may be "many"
Shelah-Soifer Graphs. No prior knowledge is required.