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The sparse regularity method for graphs with few even-cycle homomorphisms

  • Nan Zhang
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Abstract

Let Ck denote a cycle on k vertices. Pascadi (2026) established a removal lemma for C2k+1 in graphs with few C2k-homomorphisms under a dense-pairs condition, using Schatten--von Neumann norms and entropy methods. We give a short proof of a version with more restrictive partition and diagonal requirements, extending the combinatorial approach of Conlon, Fox, Sudakov and Zhao (2021) without using Pascadi's Schatten-norm regularity framework. We illustrate the method with a known sparse removal statement for odd product equations in finite groups.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026sparse,
  title = {{The sparse regularity method for graphs with few even-cycle homomorphisms}},
  author = {Nan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35421},
  eprint = {2610.35421},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35421},
}
RIS
TY  - UNPB
TI  - The sparse regularity method for graphs with few even-cycle homomorphisms
AU  - Nan Zhang
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35421
UR  - https://arxiv.org/abs/2610.35421
AB  - Let C_k denote a cycle on k vertices. Pascadi (2026) established a removal lemma for C_2k+1 in graphs with few C_2k-homomorphisms under a dense-pairs condition, using Schatten--von Neumann norms and entropy methods. We give a short proof of a version with more restrictive partition and diagonal requirements, extending the combinatorial approach of Conlon, Fox, Sudakov and Zhao (2021) without using Pascadi's Schatten-norm regularity framework. We illustrate the method with a known sparse removal statement for odd product equations in finite groups.
ER  -