The sum choice number of P3□Pn

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