{
  "abstract": "For an edge $uv$ of a finite simple graph $G$, its imbalance is $|d_G(u)-d_G(v)|$, and the imbalance multiset $M_G$ consists of the imbalances of all edges of $G$. Kozerenko and Skochko conjectured that $M_G$ is graphic whenever every edge has positive imbalance. We prove this conjecture. The main ingredient is the following capacity bound: for every set $A$ of $k$ edges, \\[ \\sum_{e\\in E(G)\\setminus A}\\min\\{k,\\operatorname{imb}_G(e)\\} \\ge k\\max\\{Δ-k,0\\}, \\] where $Δ$ is the maximum degree of $G$. This bound yields all Erdős--Gallai inequalities directly; a parity computation completes the proof.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09191",
  "author_total": 2,
  "authors": [
    {
      "name": "James Alexander Schreib"
    },
    {
      "name": "Yousof Yavari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jcfezejrh2kg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09191",
  "fulltext_url": null,
  "id": "3jcfezejrh2kg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09191",
  "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.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7202210955",
  "pdf_url": "https://arxiv.org/pdf/2608.09191",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jcfezejrh2kg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2608.09191",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09191"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Proof of the Imbalance Conjecture",
  "title_text": "A Proof of the Imbalance Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/3jcfezejrh2kg",
  "venue": "arXiv",
  "versions": []
}