Parameterized Complexity of Path Set Packing

In PATH SET PACKING, the input is an undirected graph G, a collection $$\mathcal{P}$$ of simple paths in and positive integer k. The problem to decide whether there exist k edge-disjoint . We study parameterized complexity PACKING with respect both natural structural parameters. show that W[1]-hard vertex cover plus maximum length path , pathwidth degree solution size. These results answer open question raised [17]. On side, we present FPT algorithm by feedback set degree, also provide treewidth