Fractional list packing for layered graphs

[2410.02695] Fractional list packing for layered graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2410.02695 (math) [Submitted on 3 Oct 2024 ( v1 ), last revised 8 Apr 2026 (this version, v2)] Title: Fractional list packing for layered graphs Authors: Stijn Cambie , Wouter Cames van Batenburg View a PDF of the paper titled Fractional list packing for layered graphs, by Stijn Cambie and 1 other authors View PDF Abstract: The fractional list packing number $\chi_{\ell}^{\bullet}(G)$ of a graph $G$ is a graph invariant that has recently arisen from the study of disjoint list-colourings. It measures how large the lists of a list-assignment $L:V(G)\rightarrow 2^{\mathbb{N}}$ need to be to ensure the existence of a `perfectly balanced' probability distribution on proper $L$-colourings, i.e., such that at every vertex $v$, every colour appears with equal probability $1/|L(v)|$. In this work we give various bounds on $\chi_{\ell}^{\bullet}(G)$, which admit strengthenings for correspondence and local-degree versions. As a corollary, we improve theorems on the related notion of flexible list colouring. In particular we study Cartesian products and $d$-degenerate graphs, and we prove that $\chi_{\ell}^{\bullet}(G)$ is bounded from above by the pathwidth of $G$ plus one. The correspondence analogue of the latter is false for treewidth instead of pathwidth. Comments: 21 pages; v2 accepted to Journal of Graph Theory Subjects: Combinatorics (math.CO) ; Discrete Mathematics (cs.DM); Probability (math.PR) MSC classes: 05C15, 05C70, 05c85, 05d15 Cite as: arXiv:2410.02695 [math.CO] (or arXiv:2410.02695v2 [math.CO] for this version) https://doi.org/10.48550/arXiv.2410.02695 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1002/jgt.70048 Focus to learn more DOI(s) linking to related resources Submission history From: Wouter Cames Van Batenburg [ view email ] [v1] Thu, 3 Oct 2024 17:20:13 UTC (30 KB) [v2] Wed, 8 Apr 2026 11:40:48 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Fractional list packing for layered graphs, by Stijn Cambie and 1 other authors View PDF TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2024-10 Change to browse by: cs cs.DM math math.PR 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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