[{"external_id":{"arxiv":["2301.07693"]},"article_number":"e38","author":[{"last_name":"Gishboliner","full_name":"Gishboliner, Lior","first_name":"Lior"},{"first_name":"Asaf","full_name":"Shapira, Asaf","last_name":"Shapira"},{"last_name":"Wigderson","first_name":"Yuval","full_name":"Wigderson, Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"article_processing_charge":"No","title":"An efficient asymmetric removal lemma and its limitations","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","date_published":"2025-02-10T00:00:00Z","volume":13,"oa_version":"Preprint","publisher":"Cambridge University Press","OA_place":"repository","publication":"Forum of Mathematics, Sigma","status":"public","arxiv":1,"month":"02","intvolume":"        13","publication_identifier":{"issn":["2050-5094"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2301.07693","open_access":"1"}],"doi":"10.1017/fms.2024.68","type":"journal_article","publication_status":"published","date_created":"2026-06-29T10:51:07Z","mathsc":["05C35","11B75"],"day":"10","article_type":"original","oa":1,"language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"scopus_import":"1","OA_type":"green","_id":"22158","extern":"1","date_updated":"2026-07-08T10:31:22Z","citation":{"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>.","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.","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>.","short":"L. Gishboliner, A. Shapira, Y. Wigderson, Forum of Mathematics, Sigma 13 (2025).","ista":"Gishboliner L, Shapira A, Wigderson Y. 2025. An efficient asymmetric removal lemma and its limitations. Forum of Mathematics, Sigma. 13, e38.","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>","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>"},"quality_controlled":"1"}]