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PreprintCC BY-NC-ND 4.0arXiv

On $4$-perfect-matching covers of cubic graphs with two adjacent odd circuits in a $2$-factor

  • Ján Karabáš
  • Edita Máčajová
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Abstract

Let G be a cubic graph admitting a $2$-factor consisting of exactly two odd circuits, and let the complementary $1$-factor contain precisely three spokes (along with an arbitrary number of chords). We show that four perfect matchings can cover G. As a consequence, G fulfils the 7/5-Conjecture of Alon and Tarsi.

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Cite

BibTeXRIS
BibTeX
@misc{karabas20264perfectmatching,
  title = {{On $4$-perfect-matching covers of cubic graphs with two adjacent odd circuits in a $2$-factor}},
  author = {Ján Karabáš and Edita Máčajová},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.09475},
  eprint = {2605.09475},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.09475},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On $4$-perfect-matching covers of cubic graphs with two adjacent odd circuits in a $2$-factor
AU  - Ján Karabáš
AU  - Edita Máčajová
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2605.09475
UR  - https://arxiv.org/abs/2605.09475
AB  - Let G be a cubic graph admitting a $2$-factor consisting of exactly two odd circuits, and let the complementary $1$-factor contain precisely three spokes (along with an arbitrary number of chords). We show that four perfect matchings can cover G. As a consequence, G fulfils the 7/5-Conjecture of Alon and Tarsi.
ER  -