Abstract
Consider the NP-hard problem of, given a simple graph G, to find a series-parallel subgraph of G with the maximum number of edges. The algorithm that, given a connected graph G, outputs a spanning tree of G, is a \(\frac12\)-approximation. Indeed, if n is the number of vertices in G, any spanning tree in G has n−1 edges and any series-parallel graph on n vertices has at most 2n−3 edges. We present a \(\frac{7}{12}\)-approximation for this problem and results showing the limits of our approach.
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Călinescu, G., Fernandes, C.G., Kaul, H. (2010). Maximum Series-Parallel Subgraph. In: Paul, C., Habib, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2009. Lecture Notes in Computer Science, vol 5911. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11409-0_5
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DOI: https://doi.org/10.1007/978-3-642-11409-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11408-3
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