{
  "abstract": "Shift graphs, introduced by Erdős and Hajnal in 1964, form one of the simplest known non-recursive constructions of triangle-free graphs with arbitrarily large chromatic number. In this note, we identify a surprising property: for each integer $k \\geq 1$, the smallest $k$-chromatic shift graph contains a unique induced $k$-vertex-critical subgraph. We give an explicit description of this subgraph and prove its uniqueness. This provides a new family of vertex-critical triangle-free graphs of arbitrarily large chromatic number.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Tomáš Kaiser"
    },
    {
      "name": "Matěj Stehlík"
    },
    {
      "name": "Riste Škrekovski"
    },
    {
      "name": "Bjarne Toft"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3a6qjt3ttyhn.bib",
  "cited_by": 0,
  "doi": "10.37236/15178",
  "fulltext_url": null,
  "id": "e3a6qjt3ttyhn",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33p413",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7125696755",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33p413/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/e3a6qjt3ttyhn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/15178",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33p413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Limits and Structures in Graph Theory",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Note on Vertex-Critical Induced Subgraphs of Shift Graphs",
  "title_text": "A Note on Vertex-Critical Induced Subgraphs of Shift Graphs",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/e3a6qjt3ttyhn",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}