Title: Symmetric chromatic function in star basis.

Abstract.
The Hopf algebra approach to Stanley's symmetric chromatic function of graphs 
directly leads to a simple construction of bases of the algebra of 
symmetric function. Namely, for each value of $n$ pick a connected graph 
with $n$ vertices. Then the symmetric chromatic functions of these graphs 
form a basis of the algebra of symmetric function. As a family of such 
graphs we choose stars with $n$ vertices, those are the trees which have 
one central vertex of degree $n-1$ connecting with $n-1$ leaves. I give a 
simple closed formula discovered by my student Ishaan Shah expressing the 
symmetric chromatic function of a graph in terms of this basis of symmetric 
chromatic function of stars.