{
  "abstract": "A graph $G$ is weakly $H$-saturated if one can obtain $K_n$ by adding one edge to $G$ at a time, where each additional edge creates at least one new copy of $H$. The minimum number of edges needed for a weakly $H$-saturated graph $G$ of order $n$ is known as the weak saturation number of $H$, written $wsat(n,H)$. A graph $G$ is minimum weakly saturated if $wsat(n,G)=|E(G)|-1$ for some value of $n$. We explore classes of minimum weakly saturated graphs and their connection to the $H$-bootstrap percolation process, as well as weak saturation in a more general setting than the complete graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01851",
  "author_total": 1,
  "authors": [
    {
      "name": "Roman Vasquez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/12zbsg0brgr50.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01851",
  "fulltext_url": null,
  "id": "12zbsg0brgr50",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01851",
  "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": "W7207570733",
  "pdf_url": "https://arxiv.org/pdf/2609.01851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/12zbsg0brgr50.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimum Weakly Saturated Graphs and Bootstrap Percolation in General Host Graphs",
  "title_text": "Minimum Weakly Saturated Graphs and Bootstrap Percolation in General Host Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/12zbsg0brgr50",
  "venue": "arXiv",
  "versions": []
}