{
  "abstract": "We study the bipanchromatic number $χ_B$, introduced by Lalou et al. (Discrete Appl. Math. 391 (2026), 511-522) as the maximum number of colors in a panchromatic hypergraph coloring where every color appears at least twice. They show that merging uniquely occurring colors in a maximum panchromatic coloring gives the lower bound $β=χ_P-\\lceilα/2\\rceil \\leq χ_B$, where $χ_P$ is the panchromatic number and $α$ is the minimum number of such colors among maximum panchromatic colorings. They conjectured that $χ_B=β$ and subsequently disproved it (arXiv:2610.08042). We identify the smallest counterexample, with six vertices and three hyperedges, both minimum possible. We show that the ratio bound $χ_B/β<2$ is asymptotically sharp and prove minimality results for the order and hyperedge count. For $3\\leα<χ_P$ we show that every integer from $β$ to $χ_P-1$ occurs as $χ_B$ while $χ_P$ and $α$ are held fixed. Furthermore, we discover that the values $|V|,χ_P,α$ directly decide whether the conjectured equality holds except when $α=4$, where a matching reduction resolves the ambiguity. We derive the optimal universal lower bound $L$ depending only on $|V|,χ_P,α$ in the nontrivial regime $0<2α<|V|$. Finally, we prove $χ_B/L\\le5/4$ and $χ_B/L\\le6/5+1/(5L)$, with $5/4$ sharp and $6/5$ asymptotically sharp as $L\\to\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27133",
  "author_total": 2,
  "authors": [
    {
      "name": "Stefan Novaković"
    },
    {
      "name": "Duško Jojić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0pep52d9h68jy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27133",
  "fulltext_url": null,
  "id": "0pep52d9h68jy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27133",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223116005",
  "pdf_url": "https://arxiv.org/pdf/2610.27133",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0pep52d9h68jy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27133"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counterexamples to a conjecture and improved bounds for bipanchromatic colorings",
  "title_text": "Counterexamples to a conjecture and improved bounds for bipanchromatic colorings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/0pep52d9h68jy",
  "venue": "arXiv",
  "versions": []
}