{
  "abstract": "In this paper, we generalize the concept of packing total coloring by introducing a new concept called the $S$-packing total coloring. For a graph $G$ and a non-decreasing sequence $S=(a_1,a_2,\\ldots)$ of positive integers, an $S$-packing total coloring of $G$ is a mapping $c: V(G)\\cup E(G)\\rightarrow \\{1,2,\\ldots\\}$ such that for any two distinct elements $A,B\\in V(G)\\cup E(G)$ with $c(A)=c(B)=i$, the distance between $A$ and $B$ is at least $a_i+1$. The smallest integer $k$ such that $G$ admits an $S$-packing total coloring using $k$ colors is called the $S$-packing total chromatic number of $G$, denoted by $χ_S^{''}(G)$. For any sequence $S$, we establish general lower and upper bounds for $χ_S^{''}(G)$, and characterize all graphs $G$ with $χ_S^{''}(G)\\in\\{1,2,3\\}$. Furthermore, we investigate $S$-packing total chromatic numbers of complete bipartite graphs, as well as infinite and finite paths and cycles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10107",
  "author_total": 4,
  "authors": [
    {
      "name": "Jasmina Ferme"
    },
    {
      "name": "Jaka Hedžet"
    },
    {
      "name": "Petra Melicharova"
    },
    {
      "name": "Daša Mesarič Štesl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fbvt1ra9sk6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10107",
  "fulltext_url": null,
  "id": "2fbvt1ra9sk6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10107",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7212177399",
  "pdf_url": "https://arxiv.org/pdf/2609.10107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fbvt1ra9sk6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On $S$-packing total colorings",
  "title_text": "On S-packing total colorings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/2fbvt1ra9sk6q",
  "venue": "arXiv",
  "versions": []
}