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PreprintCC BY 4.0arXiv

On nowhere-zero 3-flows in Cayley graphs on groups of order p2n

  • Milad Ahanjideh
  • István Kovács
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Abstract

We consider Tutte's $3$-flow conjecture in the class of Cayley graphs on groups G of order p2n, where p is a prime and n is square-free and coprime to p. The conjecture has been proved by J. Zhang and Z. Zhang in the case where n is a prime (Discrete Mathematics, 2023); and by the authors in the case where p=2 (arXiv:2603.24175). In this paper, we prove the conjecture in the case where p > 2 and either a Sylow p-subgroup or a Hall n-subgroup of G is a cyclic group.

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Cite

BibTeXRIS
BibTeX
@misc{ahanjideh2026nowherezero,
  title = {{On nowhere-zero $3$-flows in Cayley graphs on groups of order $p^2n$}},
  author = {Milad Ahanjideh and István Kovács},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.42099},
  eprint = {2610.42099},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.42099},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On nowhere-zero 3-flows in Cayley graphs on groups of order p^2n
AU  - Milad Ahanjideh
AU  - István Kovács
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.42099
UR  - https://arxiv.org/abs/2610.42099
AB  - We consider Tutte's $3$-flow conjecture in the class of Cayley graphs on groups G of order p^2n, where p is a prime and n is square-free and coprime to p. The conjecture has been proved by J. Zhang and Z. Zhang in the case where n is a prime (Discrete Mathematics, 2023); and by the authors in the case where p=2 (arXiv:2603.24175). In this paper, we prove the conjecture in the case where p > 2 and either a Sylow p-subgroup or a Hall n-subgroup of G is a cyclic group.
ER  -