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Space-Efficient Biconnected Components and Recognition of Outerplanar Graphs

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We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using $$O(n+\min \{m,n\log \log n\})$$O(n+min{m,nloglogn}) bits. With the same… Click to show full abstract

We present space-efficient algorithms for computing cut vertices in a given graph with n vertices and m edges in linear time using $$O(n+\min \{m,n\log \log n\})$$O(n+min{m,nloglogn}) bits. With the same time and using $$O(n+m)$$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 $$O(n\log \log n)$$O(nloglogn) time using O(n) bits.

Keywords: biconnected components; log; outerplanar graphs; space efficient

Journal Title: Algorithmica
Year Published: 2018

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