Packing the largest trees in the tree packing conjecture

[2403.10515] Packing the largest trees in the tree packing conjecture Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2403.10515 (math) [Submitted on 15 Mar 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: Packing the largest trees in the tree packing conjecture Authors: Barnabás Janzer , Richard Montgomery View a PDF of the paper titled Packing the largest trees in the tree packing conjecture, by Barnab\'as Janzer and Richard Montgomery View PDF HTML (experimental) Abstract: The famous tree packing conjecture of Gyárfás from 1976 says that any sequence of trees $T_1,\ldots,T_n$ such that $|T_i|=i$ for each $i\in [n]$ packs into the complete $n$-vertex graph $K_n$. Packing even just the largest trees in such a sequence has proven difficult, with Bollobás drawing attention to this in 1995 by conjecturing that, for each $k$, if $n$ is sufficiently large then the largest $k$ trees in any such sequence can be packed into $K_n$. This has only been shown for $k\leq 5$, by Żak, despite many partial results and much related work on the full tree packing conjecture. We prove Bollobás's conjecture, by showing that, moreover, a linear number of the largest trees can be packed in the tree packing conjecture. Comments: 34 pages, 5 figures. Version accepted for publication Subjects: Combinatorics (math.CO) Cite as: arXiv:2403.10515 [math.CO] (or arXiv:2403.10515v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2403.10515 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Richard Montgomery [ view email ] [v1] Fri, 15 Mar 2024 17:55:03 UTC (51 KB) [v2] Thu, 9 Apr 2026 20:05:26 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Packing the largest trees in the tree packing conjecture, by Barnab\'as Janzer and Richard Montgomery View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-03 Change to browse by: math 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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