{
  "abstract": "We study the connected coloring game on corona products of graphs. For connected graphs $G$ and $H$, we prove the sharp upper bound $χ_{cg}(G\\circ H)\\leq\\max\\{Δ(G),Δ(H)+1\\}+1$ and establish a further bound using the Bob-start ordinary coloring game on the second factor. We show that the difference between the Alice-start and Bob-start connected game chromatic numbers can be arbitrarily large in either direction. We further prove that a connected subgraph may have arbitrarily larger connected game chromatic number than its ambient connected graph, and that $χ_{cg}(G\\circ H)$ cannot be bounded in terms of $χ_{cg}(G)$ and $χ_{cg}(H)$ alone, even when both factors have connected game chromatic number $2$. We also obtain corona products for which the difference $χ_g-χ_{cg}$ is arbitrarily large and construct infinitely many connected graphs with $χ_g<χ_{cg}$. Finally, for corona products of trees, we prove the universal upper bound $5$, characterize those attaining the value $3$, give structural sufficient conditions for the value $4$, and exhibit a broad family attaining the value $5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29650",
  "author_total": 1,
  "authors": [
    {
      "name": "Daša Mesarič Štesl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6nfmd5yj8vtwk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29650",
  "fulltext_url": null,
  "id": "6nfmd5yj8vtwk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29650",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223228948",
  "pdf_url": "https://arxiv.org/pdf/2610.29650",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6nfmd5yj8vtwk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29650",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29650"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Connected Coloring Games on Corona Products of Graphs",
  "title_text": "Connected Coloring Games on Corona Products of Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/6nfmd5yj8vtwk",
  "venue": "arXiv",
  "versions": []
}