{
  "abstract": "We modify a construction of Bradač \\cite{Bradac26} using a vertex ordering to give, for every prime power $q$, an explicit $K_5$ free graph with more than $q^7$ vertices and independence number below $600q^4$. This shows $$r(5,t)=Ω(t^{7/4}).$$ Additionally, pruning a graph defined by the Coulter and Matthews polynomial $X^{14}$ \\cite{CM}, we give a deterministic polynomial time construction proving $$r(5,t)=Ω\\bigl(t^{20/11-\\varepsilon}\\bigr)$$ for every fixed $\\varepsilon>0$. These results improve the constructive lower bound $Ω(t^{5/3})$ of Kostochka, Pudlák and Rödl \\cite{KPR}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06969",
  "author_total": 3,
  "authors": [
    {
      "name": "Amrit Kandasamy"
    },
    {
      "name": "Lawrence Zhou"
    },
    {
      "name": "Levi Segal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fhjjbe1wkzya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06969",
  "fulltext_url": null,
  "id": "5fhjjbe1wkzya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06969",
  "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": "W7220970330",
  "pdf_url": "https://arxiv.org/pdf/2610.06969",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fhjjbe1wkzya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06969",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06969"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Improved Explicit and Algorithmic Lower Bounds for r(5,t)",
  "title_text": "Improved Explicit and Algorithmic Lower Bounds for r(5,t)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5fhjjbe1wkzya",
  "venue": "arXiv",
  "versions": []
}