A Lower Bound on the Size of Series-Parallel Graphs Dense in Long Paths

13 years 11 months ago

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One way to quantify how dense a multidag is in long paths is to find the largest n, m such that whichever n edges are removed, there is still a path from an original input to an original output with m edges - the larger we can make n, m, the denser is the graph. For a given n, m, we would like to lower bound the size such a graph, say in edges, at least when restricting to a particular class of graphs. A bound of (n lg m) was provided in [Val77] for one notion of series-parallel graphs. Here we reprove the same result but in greater detail and relate that notion of series-parallel to other popular notions of series-parallel. In particular, we show that that notion is more general than minimal series-parallel and two terminal series-parallel.

Chris Calabro

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