{
  "abstract": "Two vertices of a (not necessarily properly) arc-colored digraph are called arc-$\\ell$-color-avoiding strongly $k$-arc-connected if, after the removal of the arcs of any at most $\\ell$ colors, they remain strongly $k$-arc-connected. The arc-$\\ell$-color-avoiding strongly $k$-arc-connected components are maximal sets of vertices such that any two of those vertices belonging to the set are arc-$\\ell$-color-avoiding strongly $k$-arc-connected in the graph. We investigate the problems of finding the arc-$\\ell$-color-avoiding strongly $k$-arc-connected components and the maximal arc-$\\ell$-color-avoiding strongly $k$-arc-connected subgraphs of an arc-colored digraph. We also consider possible generalizations to $k$-vertex-connectivity and to vertex-colored digraphs. We show that despite the seemingly minor differences in definitions, the complexity of these problems varies significantly: some can be solved in polynomial time, while others are NP-hard. It also turns out that in some cases the problem is NP-hard when multiple colors can be assigned to each vertex, but the problem becomes polynomial-time solvable when each vertex is single-colored.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39982",
  "author_total": 3,
  "authors": [
    {
      "name": "Panna Tímea Fekete"
    },
    {
      "name": "Roland Molontay"
    },
    {
      "name": "Kitti Varga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tf9ms9fm8f0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39982",
  "fulltext_url": null,
  "id": "3tf9ms9fm8f0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39982",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39982",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tf9ms9fm8f0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39982",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39982"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Complexity of finding color-avoiding connected components",
  "title_text": "Complexity of finding color-avoiding connected components",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3tf9ms9fm8f0g",
  "venue": "arXiv",
  "versions": []
}