Skip to content
DraconiticResearch
Search Sources API
194,230 studies31 sourcesUpdated 44 min ago
PreprintCC BY 4.0arXiv

Strong edge-colourings of truncations of cubic graphs

  • Domenico Labbate
  • Federico Romaniello
Open at sourcePDFDOICite

Abstract

We study a problem posed by Kardoš asking whether the truncation of every connected simple bridgeless cubic graph has strong chromatic index six. The truncation T(G) is obtained by replacing each vertex of G with a triangle and attaching its incident edges to distinct vertices of that triangle. An affirmative answer was previously established for prism bases by Han and Cui. We prove that sidx(T(G))=6 whenever G is a connected simple cubic graph that is bipartite or is both bridgeless and claw-free. Both proofs are constructive and use a common compatibility criterion for combining colourings of smaller pieces. The bipartite result also extends to non-det-extremal multigraphs.

Related

  1. On-line majority edge-colourings of graphs
    Paweł Pękała
    arXivPreprintCC BY-SA 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. v-numbers of powers of edge ideals of cubic circulant graphs
    Guangjun Zhu, Jiaxin Li, Yulin Hu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Power-of-two cycles in projective cubic graphs of large edge-width
    Jean-François Culus
    HALPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsHALarXiv
  4. On Arc-Transitive Regular Covers of Cubic Edge-Primitive Graphs
    Feng Deng, Jing Jian Li, Yu Wang +1
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Cubic edge-transitive graphs of order ℓ p2
    Xue Wang, Jun-Jie Huang, Da-Wei Yang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{labbate2026strong,
  title = {{Strong edge-colourings of truncations of cubic graphs}},
  author = {Domenico Labbate and Federico Romaniello},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41950},
  eprint = {2610.41950},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41950},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strong edge-colourings of truncations of cubic graphs
AU  - Domenico Labbate
AU  - Federico Romaniello
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41950
UR  - https://arxiv.org/abs/2610.41950
AB  - We study a problem posed by Kardoš asking whether the truncation of every connected simple bridgeless cubic graph has strong chromatic index six. The truncation T(G) is obtained by replacing each vertex of G with a triangle and attaching its incident edges to distinct vertices of that triangle. An affirmative answer was previously established for prism bases by Han and Cui. We prove that sidx(T(G))=6 whenever G is a connected simple cubic graph that is bipartite or is both bridgeless and claw-free. Both proofs are constructive and use a common compatibility criterion for combining colourings of smaller pieces. The bipartite result also extends to non-det-extremal multigraphs.
ER  -