A paintability version of the combinatorial Nullstellensatz, and list colorings of -partite -uniform hypergraphs.
A tandem version of the cops and robber game played on products of graphs
In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.