{
  "abstract": "A messenger and a pursuer move alternately on a finite loopless directed graph, with complete information and waiting permitted. The messenger moves first and wins upon reaching a designated recipient, before interception there. We determine the maximum number $M(n,m)$ of ordered nonadjacent source--recipient pairs for which delivery is guaranteed against every initial pursuer position, among graphs with $n$ vertices and $m$ arcs. We give the exact value and an explicit attaining graph for every admissible pair $(n,m)$. For $n\\ge12$, a piecewise formula describes sparse growth, the interval $2n\\le m\\le n(n-3)$ in which every missing pair can be guaranteed, a dense staircase, and the zero range above $n(n-2)$. Complete finite tables cover smaller orders. The proofs combine degree and support bounds, local strategy composition, protected routing, and constructions in the missing-arc graph. Finite exceptional cases use explicit strategy certificates and complete computational exclusions. Reproducible programs and certificates accompany the paper; a Lean development verifies the complete formula for $n\\ge12$ and $m\\ge24$, the claimed scores of prescribed constructions at every admissible pair, and further finite upper bounds. Its remaining obligations are stated separately.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39469",
  "author_total": 1,
  "authors": [
    {
      "name": "Angel Ivanov Raychev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28nxqgeaf00hs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39469",
  "fulltext_url": null,
  "id": "28nxqgeaf00hs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39469",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28nxqgeaf00hs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Guaranteed indirect delivery in directed networks: The joint extremal function and explicit attaining constructions",
  "title_text": "Guaranteed indirect delivery in directed networks: The joint extremal function and explicit attaining constructions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/28nxqgeaf00hs",
  "venue": "arXiv",
  "versions": []
}