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arXiv · 2604.12370

Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs

Gregory Morse·Tamás Kozsik
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Abstract

We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering together in the fully dynamic setting is less developed. This preprint presents a framework for fully dynamic BFS in directed graphs together with supporting data structures for maintaining the BFS tree, single-source shortest paths, and single-source reachability under both insertions and deletions.

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Gregory Morse, Tamás Kozsik. 2026-04-14. Fully Dynamic Breadth First Search and Spanning Trees in Directed Graphs. https://arxiv.org/abs/2604.12370

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