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arXiv · 2601.20137

Dynamic framework for edge-connectivity maintenance of simple graphs

Blazej Wrobel
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Abstract

We present a framework for dynamically maintaining $k$-edge-connectivity of an undirected simple graph $G$ under edge insertions and deletions, where $k$ is a fixed constant. After an edge insertion, the algorithm identifies and removes a distinct redundant edge to maintain sparsity, in $O(k \log n)$ amortized time. After an edge deletion that reduces $\lambda(G)$ below $k$, the algorithm restores $k$-edge-connectivity by adding at most two new edges (excluding the deleted edge), in $O(k^{3/2} n^{3/2})$ time. The insertion procedure combines Nagamochi-Ibaraki sparse certificates with Link-Cut Trees; the deletion procedure uses a single maximum-flow computation on the sparsified graph. Throughout all updates, the graph is maintained with $O(kn)$ edges.

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Blazej Wrobel. 2026-01-27. Dynamic framework for edge-connectivity maintenance of simple graphs. https://arxiv.org/abs/2601.20137

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