{
  "abstract": "Let $\\mathcal{N}=(V,A,S, R)$ be a directed network, where $D=(V,A)$ is a digraph, $S=\\{s_1,s_2,\\ldots,s_k\\}\\subseteq V$ is a set of senders, and $R=\\{r_1,r_2,\\ldots,r_k\\}\\subseteq V$ is a set of receivers. We prove that if, for each $1\\le j \\le k$, there exist $k$ pairwise arc-disjoint directed paths in $D$, one from each $s_i$ to $r_j$, then the underlying undirected network of ${\\cal N}$, with unit capacities, admits a feasible $(s_1,s_2,\\ldots,s_k)$-$(r_1,r_2,\\ldots,r_k)$ multiflow of value $1$ for each pair $(s_i,r_i)$, $i=1,2,\\ldots,k$. This establishes the multiple unicast conjecture proposed by Langberg and Médard in 2009.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33497",
  "author_total": 4,
  "authors": [
    {
      "name": "Kai Cai"
    },
    {
      "name": "Guangyue Han"
    },
    {
      "name": "Mengxi Yang"
    },
    {
      "name": "Wenan Zang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ea5dp5qmxax17.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33497",
  "fulltext_url": null,
  "id": "ea5dp5qmxax17",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33497",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7224025453",
  "pdf_url": "https://arxiv.org/pdf/2610.33497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ea5dp5qmxax17.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proof of the Langberg-Médard Multiple Unicast Conjecture",
  "title_text": "Proof of the Langberg-Médard Multiple Unicast Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ea5dp5qmxax17",
  "venue": "arXiv",
  "versions": []
}