Bitonic Sorting Network

To establish a lower bound on the parceling number of S n we show that, under certain conditions , the parceling number of a graph is no less than the parceling number of its subgraph. For a directed graph G, G 0 is a convex sub-graph of G if for any directed path t of G whose endpoints are both in G 0 : all the nodes and edges of t are in G 0. Note, for example, that any slice of a dil-graph is a convex subgraph.