Sum list coloring \(2\times n\) arrays (Q698613)

Summary: A graph is \(f\)-choosable if for every collection of lists with list sizes specified by \(f\) there is a proper coloring using colors from the lists. The sum choice number is the minimum over all choosable functions \(f\) of the sum of the sizes in \(f\). We show that the sum choice number of a \(2 \times n\) array (equivalent to list edge coloring \(K_{2,n}\) and to list vertex coloring the Cartesian product \(K_2 \square K_n\)) is \(n^2 + \lceil 5n/3 \rceil\).