Abstract
In this paper, we present the Generalized Packing Problem (GPF) in graphs in such a way that all other packing problems in graphs presented in the literature correspond to particular instances of it. We find the first class of graphs where one of these previously defined packing problems is tractable and another is NP-hard. We show that GPF remains linear-time solvable in strongly chordal graphs and, when reduced to instances with bounded neighborhood capacities (M-GPF), remains polynomial-time solvable in bounded clique-width graphs. To design specific algorithms that take advantage of the structural properties of certain subclasses of bounded clique-width graphs, we obtain technical results related to the behavior of the new packing parameter under several graph operations. In particular, we present a linear-time algorithm to solve GPF in block graphs and a polynomial-time algorithm to solve M-GPF in P4-tidy graphs.
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