{
  "abstract": "A graph $H$ is called common if the number of monochromatic copies of $H$ in a $2$-edge-coloring of a large complete graph is asymptotically minimized by the random coloring with an equal proportion of each color. The house graph and $K_4$ with one edge subdivided once are known to be common by the flag algebra method. Grzesik, Lee, Lidický, and Volec asked for ``human-friendly'' proofs of the commonality of these two graphs. In this short note, we give flag-algebra-free proofs that both graphs are common.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20149",
  "author_total": 1,
  "authors": [
    {
      "name": "Hao Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/76hfm46a95q2r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20149",
  "fulltext_url": null,
  "id": "76hfm46a95q2r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20149",
  "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",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7221852027",
  "pdf_url": "https://arxiv.org/pdf/2610.20149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/76hfm46a95q2r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Elementary Proofs of Commonality of the House Graph and $K_4$ with One Edge Subdivided",
  "title_text": "Elementary Proofs of Commonality of the House Graph and K_4 with One Edge Subdivided",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/76hfm46a95q2r",
  "venue": "arXiv",
  "versions": []
}