Complexity of Firefighting on Graphs

[2505.11082] Complexity of Firefighting on Graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computational Complexity arXiv:2505.11082 (cs) [Submitted on 16 May 2025 ( v1 ), last revised 14 Apr 2026 (this version, v4)] Title: Complexity of Firefighting on Graphs Authors: Julius Althoetmar , Jamico Schade , Torben Schürenberg View a PDF of the paper titled Complexity of Firefighting on Graphs, by Julius Althoetmar and 2 other authors View PDF HTML (experimental) Abstract: We consider a pursuit-evasion game that describes the process of extinguishing a fire burning on the nodes of an undirected graph. We denote the minimum number of firefighters required by ffn(G) and provide almost sharp bounds to this graph parameter for complete binary trees. We show that deciding whether ffn(G) <= m for given G and m is NP-hard. Furthermore, we show that shortest strategies can have superpolynomial length, leaving open whether the problem is in NP. We provide a construction that allows for transferring these results to a well-established Cops and Robbers variant called the "Hunter and Rabbit game". Comments: Full version of the paper accepted at WG 2026 Subjects: Computational Complexity (cs.CC) ; Discrete Mathematics (cs.DM) MSC classes: 05Cxx ACM classes: F.2.2; G.2.2 Cite as: arXiv:2505.11082 [cs.CC] (or arXiv:2505.11082v4 [cs.CC] for this version) https://doi.org/10.48550/arXiv.2505.11082 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Torben Schürenberg [ view email ] [v1] Fri, 16 May 2025 10:13:30 UTC (54 KB) [v2] Tue, 20 May 2025 16:03:14 UTC (54 KB) [v3] Tue, 3 Jun 2025 06:44:25 UTC (54 KB) [v4] Tue, 14 Apr 2026 09:16:11 UTC (122 KB) Full-text links: Access Paper: View a PDF of the paper titled Complexity of Firefighting on Graphs, by Julius Althoetmar and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.CC < prev | next > new | recent | 2025-05 Change to browse by: cs cs.DM References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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