Packing paths: Recycling saves time

We consider packing problems in graphs under a parameterized perspective. Starting from a maximal path packing PP of size jj we use extremal arguments for determining how many vertices of PP appear in a path packing of size j+1j+1. Generally, one can re-use 2j2j vertices of jj paths of length three, four and five. This is improved to 3j3j, 2.5j2.5j and 3j3j vertices.