---
OA_place: repository
OA_type: green
_id: '22158'
abstract:
- lang: eng
  text: "The triangle removal states that if G contains  edge-disjoint triangles,
    then G contains  triangles. Unfortunately, there are no sensible bounds on the
    order of growth of , and at any rate, it is known that  is not polynomial in .
    Csaba recently obtained an asymmetric variant of the triangle removal, stating
    that if G contains  edge-disjoint triangles, then G contains  copies of . To this
    end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following
    results:\r\n\r\n• We first give a regularity-free proof of Csaba’s theorem, which
    improves the number of copies of  to the optimal number .\r\n\r\n• We say that
    H is -abundant if every graph containing  edge-disjoint triangles has  copies
    of H. It is easy to see that a -abundant graph must be triangle-free and tripartite.
    Given our first result, it is natural to ask if all triangle-free tripartite graphs
    are -abundant. Our second result is that assuming a well-known conjecture of Ruzsa
    in additive number theory, the answer to this question is negative.\r\n\r\nOur
    proofs use a mix of combinatorial, number-theoretic, probabilistic and Ramsey-type
    arguments."
article_number: e38
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lior
  full_name: Gishboliner, Lior
  last_name: Gishboliner
- first_name: Asaf
  full_name: Shapira, Asaf
  last_name: Shapira
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: Gishboliner L, Shapira A, Wigderson Y. An efficient asymmetric removal lemma
    and its limitations. <i>Forum of Mathematics, Sigma</i>. 2025;13. doi:<a href="https://doi.org/10.1017/fms.2024.68">10.1017/fms.2024.68</a>
  apa: Gishboliner, L., Shapira, A., &#38; Wigderson, Y. (2025). An efficient asymmetric
    removal lemma and its limitations. <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/fms.2024.68">https://doi.org/10.1017/fms.2024.68</a>
  chicago: Gishboliner, Lior, Asaf Shapira, and Yuval Wigderson. “An Efficient Asymmetric
    Removal Lemma and Its Limitations.” <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press, 2025. <a href="https://doi.org/10.1017/fms.2024.68">https://doi.org/10.1017/fms.2024.68</a>.
  ieee: L. Gishboliner, A. Shapira, and Y. Wigderson, “An efficient asymmetric removal
    lemma and its limitations,” <i>Forum of Mathematics, Sigma</i>, vol. 13. Cambridge
    University Press, 2025.
  ista: Gishboliner L, Shapira A, Wigderson Y. 2025. An efficient asymmetric removal
    lemma and its limitations. Forum of Mathematics, Sigma. 13, e38.
  mla: Gishboliner, Lior, et al. “An Efficient Asymmetric Removal Lemma and Its Limitations.”
    <i>Forum of Mathematics, Sigma</i>, vol. 13, e38, Cambridge University Press,
    2025, doi:<a href="https://doi.org/10.1017/fms.2024.68">10.1017/fms.2024.68</a>.
  short: L. Gishboliner, A. Shapira, Y. Wigderson, Forum of Mathematics, Sigma 13
    (2025).
date_created: 2026-06-29T10:51:07Z
date_published: 2025-02-10T00:00:00Z
date_updated: 2026-07-08T10:31:22Z
day: '10'
doi: 10.1017/fms.2024.68
extern: '1'
external_id:
  arxiv:
  - '2301.07693'
intvolume: '        13'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2301.07693
mathsc:
- 05C35
- 11B75
month: '02'
oa: 1
oa_version: Preprint
publication: Forum of Mathematics, Sigma
publication_identifier:
  issn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: An efficient asymmetric removal lemma and its limitations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2025'
...