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This extends the previous results on the maximum number of pentagons in triangle\u2010free graphs, conjectured by Erd\u0151s in 1984, and asymptotically determines the generalized Tur\u00e1n number for odd . In contrary to the previous results on the pentagon case, our proof is not computer\u2010assisted.<\/jats:p>","DOI":"10.1002\/jgt.22738","type":"journal-article","created":{"date-parts":[[2021,9,9]],"date-time":"2021-09-09T07:05:26Z","timestamp":1631171126000},"page":"240-246","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the maximum number of odd cycles in graphs without smaller odd cycles"],"prefix":"10.1002","volume":"99","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2770-7180","authenticated-orcid":false,"given":"Andrzej","family":"Grzesik","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science Jagiellonian University Krak\u00f3w Poland"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8904-4485","authenticated-orcid":false,"given":"Bart\u0142omiej","family":"Kielak","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science Jagiellonian University Krak\u00f3w Poland"},{"name":"Institute of Mathematics of the Polish Academy of Sciences Warszawa Poland"}]}],"member":"311","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2016.03.004"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2015.08.006"},{"key":"e_1_2_5_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.08.016"},{"key":"e_1_2_5_5_1","unstructured":"P.Erd\u0151s \u00a0On some problems in graph theory combinatorial analysis and combinatorial number theory Graph Theory and Combinatorics Proc. 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