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arXiv · 2608.10848

Connectivity Augmentation of Plane Graphs

Krishnan Dehaleesan·Asif Khan·Pranabendu Misra
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Abstract

We study the problem of connectivity augmentation of a planar graph, while preserving planarity. This problem is motivated by many real-world settings such as road-networks, power-networks etc. In these settings, it is crucial to preserve the original planar embedding after augmentation. In 2009, Gutwenger and Mutzel gave a constructive algorithm showing that a connected planar graph with a fixed embedding (a plane graph) can be optimally augmented to a biconnected graph without crossings while preserving the embedding. We further this line of research, by giving an algorithm that computes a minimum set of edges that makes a connected plane graph 2-edge-connected in \(O(|V|(1+\alpha(|V|)))\) time and linear space, where \(\alpha\) is the inverse Ackermann function.

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Krishnan Dehaleesan, Asif Khan, Pranabendu Misra. 2026-08-11. Connectivity Augmentation of Plane Graphs. https://arxiv.org/abs/2608.10848

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