{
  "abstract": "An $(s,p)$-edge-coloring of a graph $G$ is an edge coloring using $s$ colors such that exactly $p$ colors appear at each vertex. To generalize the notion of proper edge-coloring, these colorings are defined to be equitable: the numbers of edges of each color incident to a vertex are fairly distributed. We find the necessary and sufficient conditions for embedding an equitable $(s_1,p_1)$-edge-coloring of $K_{n_1}$ into an equitable $(s_2,p_2)$-edge-coloring of $K_{n_2}$. We focus on the values of $n_1$, $p_1$, $n_2$, and $p_2$ where $s_1$ is necessarily larger than $p_1$ and $s_2$ is necessarily larger than $p_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07546",
  "author_total": 3,
  "authors": [
    {
      "name": "Stacie Baumann"
    },
    {
      "name": "Mika Olufemi"
    },
    {
      "name": "Stafford Yerger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dfsrs00mn4fme.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07546",
  "fulltext_url": null,
  "id": "dfsrs00mn4fme",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07546",
  "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",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7220911656",
  "pdf_url": "https://arxiv.org/pdf/2610.07546",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dfsrs00mn4fme.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07546",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07546"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Embedding equitable (s,p)-edge-colorings of $K_n$",
  "title_text": "Embedding equitable (s,p)-edge-colorings of K_n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/dfsrs00mn4fme",
  "venue": "arXiv",
  "versions": []
}