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PreprintarXiv licencearXiv

Integer Flows on Cyclic Covers of Graphs

  • Rong Luo
  • Yuying Ma
  • D. Christopher Stephens
  • Dong Ye
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Abstract

Graph covers preserve the local structure of a graph while allowing its global structure to change substantially. In this paper, we study how such changes in cyclic covers affect nowhere-zero flow properties. For a fixed integer ℓ ≥ 2, we show that for every bridgeless graph G, there exists an ℓ-fold cyclic cover of G that admits a nowhere-zero $3$-flow if ℓ is even and a nowhere-zero $4$-flow if ℓ is odd. These bounds are best possible in general. For odd ℓ, we further investigate which bridgeless graphs admit an ℓ-fold cyclic cover with a nowhere-zero $3$-flow.

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Cite

BibTeXRIS
BibTeX
@misc{luo2026integer,
  title = {{Integer Flows on Cyclic Covers of Graphs}},
  author = {Rong Luo and Yuying Ma and D. Christopher Stephens and Dong Ye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29125},
  eprint = {2610.29125},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29125},
}
RIS
TY  - UNPB
TI  - Integer Flows on Cyclic Covers of Graphs
AU  - Rong Luo
AU  - Yuying Ma
AU  - D. Christopher Stephens
AU  - Dong Ye
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29125
UR  - https://arxiv.org/abs/2610.29125
AB  - Graph covers preserve the local structure of a graph while allowing its global structure to change substantially. In this paper, we study how such changes in cyclic covers affect nowhere-zero flow properties. For a fixed integer ℓ ≥ 2, we show that for every bridgeless graph G, there exists an ℓ-fold cyclic cover of G that admits a nowhere-zero $3$-flow if ℓ is even and a nowhere-zero $4$-flow if ℓ is odd. These bounds are best possible in general. For odd ℓ, we further investigate which bridgeless graphs admit an ℓ-fold cyclic cover with a nowhere-zero $3$-flow.
ER  -