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TR08-110 | 19th November 2008 00:00

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


Authors: Chris Calabro
Publication: 16th December 2008 11:26
Downloads: 1533


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 Ω(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

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