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Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

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Abstract

We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using \(O(n+\min \{m,n\log \log n\})\) bits. With the same time and using \(O(n+m)\) bits, we can compute the biconnected components of a graph. We use this result to show an algorithm for the recognition of (maximal) outerplanar graphs in \(O(n\log \log n)\) time using O(n) bits.

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Notes

  1. Sysło [29] uses instead of chain the term maximal series of edges.

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Authors and Affiliations

  1. MNI, Technische Hochschule Mittelhessen, Gießen, Germany

    Frank Kammer

  2. LITA, Université de Lorraine, Metz, France

    Dieter Kratsch

  3. Institut für Informatik, Universität Augsburg, Augsburg, Germany

    Moritz Laudahn

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  1. Frank Kammer
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  2. Dieter Kratsch
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  3. Moritz Laudahn
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Correspondence to Frank Kammer.

Additional information

A preliminary version of this paper appeared in [22].

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Kammer, F., Kratsch, D. & Laudahn, M. Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs. Algorithmica 81, 1180–1204 (2019). https://doi.org/10.1007/s00453-018-0464-z

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