{
  "abstract": "The List Edge-Coloring Conjecture predicts that any graph whose edges can be colored with $k$ colors can also be colored from arbitrary lists of $k$ colors. We prove its stronger online form for two new infinite families, $K_{p-1}$ and $K_{2p}$, where $p$ is an odd prime. For even $n$, order the vertices of $K_n$ and draw each perfect matching as arcs above them. Count crossings separately within each matching, and let $S_n$ be the number of decompositions into perfect matchings having an even total crossing count minus the number having an odd total. Then \\[ S_{p-1}\\equiv\\left(\\frac{-2}{p}\\right)\\pmod p, \\qquad S_{2p}\\equiv-p\\pmod {p^2}. \\] The two congruences are governed by the same elementary matching sum over $\\F_p$, although their proofs use the prime $p$ differently. Their nonzero residues give the conjectured values even in the online game. They also treat the corresponding complete graphs with one perfect matching removed, as well as $K_{2p}$ after deleting some, but not all, of a natural cyclic family of $p$ disjoint perfect matchings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22895",
  "author_total": 1,
  "authors": [
    {
      "name": "Amir Jafari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25tdp3q7xxxdn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22895",
  "fulltext_url": null,
  "id": "25tdp3q7xxxdn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22895",
  "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|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7204209366",
  "pdf_url": "https://arxiv.org/pdf/2608.22895",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25tdp3q7xxxdn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.22895",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22895"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The List Edge-Coloring Conjecture for New Infinite Families",
  "title_text": "The List Edge-Coloring Conjecture for New Infinite Families",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/25tdp3q7xxxdn",
  "venue": "arXiv",
  "versions": []
}