The sum choice number of P3□Pn

A graph GG is said to be ff-choosable if there exists a proper coloring from every assignment of lists of colors to the vertices of GG where the list sizes are given by ff. The sum choice number of GG is the minimum ∑v∈V(G)f(v)∑v∈V(G)f(v) over all ff such that GG is ff-choosable. Here we determine the sum choice of the Cartesian product P3□Pn to be 8n−3−⌊n/3⌋8n−3−⌊n/3⌋. The techniques used here have applicability to choosability of other graphs.