{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:18Z","timestamp":1787321118616,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/100005376","name":"American Mathematical Society","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005376","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010665","name":"H2020 Marie Sklodowska-Curie Actions","doi-asserted-by":"publisher","award":["CoSP-GA 823748"],"award-info":[{"award-number":["CoSP-GA 823748"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["823748"],"award-info":[{"award-number":["823748"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["2023464"],"award-info":[{"award-number":["2023464"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003443","name":"Ministry of Education and Science of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2019-1926"],"award-info":[{"award-number":["075-15-2019-1926"]}],"id":[{"id":"10.13039\/501100003443","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1953946"],"award-info":[{"award-number":["DMS-1953946"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006260","name":"Technion-Israel Institute of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006260","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006221","name":"United States - Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2006099"],"award-info":[{"award-number":["2006099"]}],"id":[{"id":"10.13039\/100006221","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We prove that every family of (not necessarily distinct) odd cycles $O_1, \\dots, O_{2\\lceil n\/2 \\rceil-1}$ in the complete graph $K_n$ on $n$ vertices has a rainbow odd cycle (that is, a set of edges from distinct $O_i$'s, forming an odd cycle). As part of the proof, we characterize those families of $n$ odd cycles in $K_{n+1}$ that do not have any rainbow odd cycle. We also characterize those families of $n$ cycles in $K_{n+1}$, as well as those of $n$ edge-disjoint nonempty subgraphs of $K_{n+1}$, without any rainbow cycle.<\/jats:p>","DOI":"10.1137\/20m1380557","type":"journal-article","created":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T12:06:25Z","timestamp":1633349185000},"page":"2293-2303","source":"Crossref","is-referenced-by-count":7,"title":["Rainbow Odd Cycles"],"prefix":"10.1137","volume":"35","author":[{"given":"Ron","family":"Aharoni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph","family":"Briggs","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4629-410X","authenticated-orcid":true,"given":"Ron","family":"Holzman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zilin","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.37236\/208"},{"key":"atypb2","unstructured":"R. Aharoni, J. Briggs, J. Kim, and M. Kim,\n                      Rainbow Independent Sets in Certain Classes of Graphs\n                      , preprint,arXiv:1909.13143, 2019."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-019-4019-y"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2017.08.008"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90115-7"},{"key":"atypb6","doi-asserted-by":"crossref","unstructured":"K. B\u00e9rczi and T. Schwarcz,\n                      Rainbow and Monochromatic Circuits and Cuts in Binary Matroids\n                      , preprint,arXiv:2012.05037, 2021.","DOI":"10.1016\/j.disc.2022.112830"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1998.2894"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-019-02102-6"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"J. Kim, M. Kim, and O. Kwon,\n                      Rainbow independent sets on dense graph classes\n                      , Discrete Appl. Math., 2021, in press,https:\/\/doi.org\/10.1016\/j.dam.2021.04.007.","DOI":"10.1016\/j.dam.2021.04.007"},{"key":"atypb10","first-page":"39","volume":"84","author":"Kim M.","year":"2020","journal-title":"S\u00e9m. Lothar. Combin."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/os-13.1.83"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1380557","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:06:01Z","timestamp":1787317561000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1380557"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1380557"],"URL":"https:\/\/doi.org\/10.1137\/20m1380557","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}