Reachability in arborescence packings

Fortier et al. proposed several research problems on packing arborescences and settled some of them. Others were later solved by Matsuoka Tanigawa Gao Yang. The last open problem is in this article. We show how to turn an inductive idea used the latter two articles into a simple proof technique that allows relate previous results arborescence packings. prove strong version Edmonds’ theorem spanning implies Kamiyama, Katoh Takizawa’s result reachability Durand de Gevigney, Nguyen Szigeti’s matroid-based Király’s matroid-reachability-based arborescences. Further, we deduce new mixed hyperarborescences from due al.. Finally, deal with algorithmic aspects considered. first obtain algorithms find desired packings all settings then apply weighted matroid intersection algorithm also solutions minimizing given weight function.