{
  "abstract": "Let $G$ be a graph and $w_k(G)$ denote the number of walks in $G$ of length $k$. For sequences $a_1, \\cdots, a_n$ and $b_1, \\cdots, b_n$ of non-negative integers such that $a_1 + \\cdots + a_n = b_1 + \\cdots + b_n$, we determine a simple necessary and sufficient condition on $a_1, \\cdots, a_n, b_1, \\cdots, b_n$ for the inequality \\[ w_{a_1}(G) \\cdots w_{a_n}(G) \\geq w_{b_1}(G) \\cdots w_{b_n}(G) \\] to hold for any graph $G$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11846",
  "author_total": 1,
  "authors": [
    {
      "name": "Chase Wilson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31c5p9ka880ds.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11846",
  "fulltext_url": null,
  "id": "31c5p9ka880ds",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11846",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7212306889",
  "pdf_url": "https://arxiv.org/pdf/2609.11846",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31c5p9ka880ds.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11846",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11846"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A General Inequality for Walks in Graphs",
  "title_text": "A General Inequality for Walks in Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/31c5p9ka880ds",
  "venue": "arXiv",
  "versions": []
}