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PreprintarXiv licencearXiv

Extremal graphs without cycles of length 0 modulo 4

  • Yanan Hu
  • Leilei Zhang
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Abstract

In a remarkable recent result, Győri, Li, Salia, Tompkins, Varga and Zhu determined the maximum size in a graph of given order and containing no cycle of length divisible by 4. In this paper, we give a complete characterization of all graphs attaining this maximum. This answers a question posed by Li, Pan and Shi. Very recently, Chu, Park and Ryu established a sharp upper bound on the number of edges in a 2-connected graph containing no cycle of length divisible by 4. We also give a complete characterization of all such graphs attaining this bound.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026extremal,
  title = {{Extremal graphs without cycles of length 0 modulo 4}},
  author = {Yanan Hu and Leilei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28225},
  eprint = {2610.28225},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28225},
}
RIS
TY  - UNPB
TI  - Extremal graphs without cycles of length 0 modulo 4
AU  - Yanan Hu
AU  - Leilei Zhang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28225
UR  - https://arxiv.org/abs/2610.28225
AB  - In a remarkable recent result, Győri, Li, Salia, Tompkins, Varga and Zhu determined the maximum size in a graph of given order and containing no cycle of length divisible by 4. In this paper, we give a complete characterization of all graphs attaining this maximum. This answers a question posed by Li, Pan and Shi. Very recently, Chu, Park and Ryu established a sharp upper bound on the number of edges in a 2-connected graph containing no cycle of length divisible by 4. We also give a complete characterization of all such graphs attaining this bound.
ER  -