Limited Packings in Graphs

We define a k-limited packing in a graph, which generalizes a packing in a graph, and give several bounds on the size of a k-limited packing. One such bound involves the domination number of the graph, and here we show, when k=2, that all trees attaining the bound can be built via a simple sequence of operations. We also consider graphs where every maximal 2-limited packing is a maximum 2-limited packing, and characterize those of girth 14 or more.