Limited packings in graphs

We define a kk-limited packing in a graph, which generalizes a 2-packing in a graph, and give several bounds on the size of a kk-limited packing. One such bound involves the domination number of the graph, and here we show all trees attaining the bound can be built via a simple sequence of operations. We consider graphs where every maximal 2-limited packing is a maximum 2-limited packing, and characterize their structure in a number of cases.