{"issue":"12","volume":130,"publication":"European Journal of Combinatorics","has_accepted_license":"1","abstract":[{"lang":"eng","text":"The pseudoforest version of the Strong Nine Dragon Tree Conjecture states that if a graph G has maximum average degree mad(G) = 2 maxH⊆G e(H)/v(H) at most 2(k + d/d+k+1), then it has a decomposition into k + 1 pseudoforests where in one pseudoforest F the components of F have at most d edges. This was proven in 2020 in Grout and Moore (2020). We strengthen this\r\ntheorem by showing that we can find such a decomposition where additionally F is acyclic, the diameter of the components of F is at most 2ℓ + 2, where ℓ =⌊d−1/k+1⌋, and at most 2ℓ + 1 if\r\nd ≡ 1 mod (k + 1). Furthermore, for any component K of F and any z ∈ N, we have diam(K) ≤ 2z if e(K) ≥ d − z(k − 1) + 1. We also show that both diameter bounds are best possible as an\r\nextension for both the Strong Nine Dragon Tree Conjecture for pseudoforests and its original conjecture for forests. In fact, they are still optimal even if we only enforce F to have any constant maximum degree, instead of enforcing every component of F to have at most d edges."}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.ejc.2025.104214"}],"tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Elsevier","intvolume":"       130","month":"07","corr_author":"1","acknowledgement":"This work was completed while Benjamin Moore was a postdoc at Charles University, supported by project 22-17398S (Flows and cycles in graphs on surfaces) of Czech Science Foundation, Czechia.","PlanS_conform":"1","OA_place":"publisher","oa_version":"Published Version","arxiv":1,"title":"Beyond the pseudoforest strong Nine Dragon Tree theorem","external_id":{"isi":["001529769300002"],"arxiv":["2310.00931"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","_id":"20320","isi":1,"article_type":"original","publication_status":"epub_ahead","OA_type":"hybrid","oa":1,"scopus_import":"1","doi":"10.1016/j.ejc.2025.104214","department":[{"_id":"MaKw"}],"ddc":["500"],"date_updated":"2025-09-30T14:37:49Z","date_created":"2025-09-10T05:36:50Z","year":"2025","article_number":"104214","quality_controlled":"1","status":"public","language":[{"iso":"eng"}],"day":"08","type":"journal_article","article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Sebastian","full_name":"Mies, Sebastian","last_name":"Mies"},{"full_name":"Moore, Benjamin","last_name":"Moore","first_name":"Benjamin","id":"6dc1a1be-bf1c-11ed-8d2b-d044840f49d6"},{"full_name":"Smith-Roberge, Evelyne","last_name":"Smith-Roberge","first_name":"Evelyne"}],"publication_identifier":{"issn":["0195-6698"]},"citation":{"ista":"Mies S, Moore B, Smith-Roberge E. 2025. Beyond the pseudoforest strong Nine Dragon Tree theorem. European Journal of Combinatorics. 130(12), 104214.","short":"S. Mies, B. Moore, E. Smith-Roberge, European Journal of Combinatorics 130 (2025).","mla":"Mies, Sebastian, et al. “Beyond the Pseudoforest Strong Nine Dragon Tree Theorem.” <i>European Journal of Combinatorics</i>, vol. 130, no. 12, 104214, Elsevier, 2025, doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104214\">10.1016/j.ejc.2025.104214</a>.","ama":"Mies S, Moore B, Smith-Roberge E. Beyond the pseudoforest strong Nine Dragon Tree theorem. <i>European Journal of Combinatorics</i>. 2025;130(12). doi:<a href=\"https://doi.org/10.1016/j.ejc.2025.104214\">10.1016/j.ejc.2025.104214</a>","chicago":"Mies, Sebastian, Benjamin Moore, and Evelyne Smith-Roberge. “Beyond the Pseudoforest Strong Nine Dragon Tree Theorem.” <i>European Journal of Combinatorics</i>. Elsevier, 2025. <a href=\"https://doi.org/10.1016/j.ejc.2025.104214\">https://doi.org/10.1016/j.ejc.2025.104214</a>.","apa":"Mies, S., Moore, B., &#38; Smith-Roberge, E. (2025). Beyond the pseudoforest strong Nine Dragon Tree theorem. <i>European Journal of Combinatorics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.ejc.2025.104214\">https://doi.org/10.1016/j.ejc.2025.104214</a>","ieee":"S. Mies, B. Moore, and E. Smith-Roberge, “Beyond the pseudoforest strong Nine Dragon Tree theorem,” <i>European Journal of Combinatorics</i>, vol. 130, no. 12. Elsevier, 2025."},"date_published":"2025-07-08T00:00:00Z"}