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Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

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. 1.

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

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Correspondence to Frank Kammer.

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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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Keywords

  • Graph algorithms
  • Space efficiency
  • Cut vertices
  • Biconnected components
  • (Maximal)outerplanar graphs