  Let G=(V,E) be a graph and let f be a function that assigns list sizes to the
vertices of G. It is said that G is f-choosable if for every assignment of
lists of colors to the vertices of G for which the list sizes agree with f,
there exists a proper coloring of G from the lists. The sum choice number is
the minimum of the sum of list sizes for f over all choosable functions f for
G. The sum choice number of a graph is always at most the sum |V|+|E|. When the
sum choice number of G is equal to this upper bound, G is said to be sc-greedy.
In this paper, we determine the sum choice number of all graphs on five
vertices, show that trees of cycles are sc-greedy, and present some new general
results about sum list coloring.
