{
  "abstract": "Let $G$ be a finite simple graph. An averaging operation selects a nonempty connected vertex set and replaces the weights of its vertices by their arithmetic mean. For a nonnegative initial weight function $ω:V(G)\\to\\mathbb R_{\\ge0}$ and a target vertex $x$, let $t(G,x,ω)$ denote the minimum number of averaging operations needed to attain the maximum reachable weight at $x$. Gollin et al.[1] proved, using the Axiom of Choice, that a finite optimal strategy exists for every finite graph, every nonnegative initial weight function and every target vertex; see Tao [2] for a simplified proof. We prove that the lengths of shortest optimal strategies on $3$-spiders have no uniform finite bound. In particular, these lengths cannot be bounded in terms of the maximum degree of the graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31499",
  "author_total": 3,
  "authors": [
    {
      "name": "Guanheng Chen"
    },
    {
      "name": "Ran Tao"
    },
    {
      "name": "Tianyi Tao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79rm7qvrc7m5y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31499",
  "fulltext_url": null,
  "id": "79rm7qvrc7m5y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31499",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7223363253",
  "pdf_url": "https://arxiv.org/pdf/2610.31499",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79rm7qvrc7m5y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31499",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31499"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Water Transport on 3-Spiders: Unbounded Lengths of Shortest Optimal Strategies",
  "title_text": "Water Transport on 3-Spiders: Unbounded Lengths of Shortest Optimal Strategies",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/79rm7qvrc7m5y",
  "venue": "arXiv",
  "versions": []
}