{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:02Z","timestamp":1787321102026,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"Institute for Mathematics and its Applications with funds provided by the National Science Foundation","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]},{"DOI":"10.13039\/501100001711","name":"SNSF","doi-asserted-by":"crossref","award":["200021-149111"],"award-info":[{"award-number":["200021-149111"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]},{"name":"USA-Israeli BSF grant","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]},{"name":"ISF grant","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2016,1]]},"abstract":"<jats:p>A conjecture of Bandelt and Dress states that the maximum quartet distance between any two phylogenetic trees on $n$ leaves is at most $(\\frac{2}{3}+o(1))\\binom{n}{4}$. Using the machinery of flag algebras, we improve the currently known bounds regarding this conjecture; in particular, we show that the maximum is at most $(0.69+o(1))\\binom{n}{4}$. We also give further evidence that the conjecture is true by proving that the maximum distance between caterpillar trees is at most $(\\frac{2}{3}+o(1))\\binom{n}{4}$.<\/jats:p>","DOI":"10.1137\/15m1041754","type":"journal-article","created":{"date-parts":[[2016,4,14]],"date-time":"2016-04-14T13:41:17Z","timestamp":1460641277000},"page":"718-735","source":"Crossref","is-referenced-by-count":11,"title":["On the Maximum Quartet Distance between Phylogenetic Trees"],"prefix":"10.1137","volume":"30","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Humberto","family":"Naves","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benny","family":"Sudakov","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2016,4,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"N. Alon, S. Snir, and R. Yuster,\n                      On the compatibility of quartet trees\n                      , in Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 535-545, http:\/\/dx.doi.org\/10.1137\/1.9781611973402.40 doi:10.1137\/1.9781611973402.40.","DOI":"10.1137\/1.9781611973402.40"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548310000222"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000820"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(86)90038-2"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00235-2"},{"key":"atypb6","first-page":"313","author":"Berry V.","year":"1999","journal-title":"Berlin"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044-8317.1981.tb00626.x"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.02.003"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.2307\/sysbio\/34.2.193"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.endm.2013.07.029"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2012.12.008"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1998.743492"},{"key":"atypb13","first-page":"196","author":"John K. St.","year":"2001","journal-title":"Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"P. Keevash,\n                      Hypergraph Tura\u0301n problems\n                      , in Surveys in Combinatorics 2011, Cambridge University Press, Cambridge, UK, 2011, pp. 83-139, http:\/\/dx.doi.org\/10.1017\/CBO9781139004114.004 doi:10.1017\/CBO9781139004114.004.","DOI":"10.1017\/CBO9781139004114.004"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"D. R. Maddison and K.S. Schulz, eds.\n                      The Tree of Life Web Project\n                      , u\u0306lhttp:\/\/tolweb.org, 2007.","DOI":"10.11646\/zootaxa.1668.1.4"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548313000357"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548312000508"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1203350785"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548308009085"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/090747476"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"C. Semple and M. A. Steel,\n                      Phylogenetics\n                      , Oxford University Press, Oxford, UK, 2003.","DOI":"10.1093\/oso\/9780198509424.001.0001"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2008.133"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1137\/11086964X"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/BF02618470"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1093\/oxfordjournals.molbev.a025664"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1041754","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:04:48Z","timestamp":1787317488000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1041754"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["10.1137\/15M1041754"],"URL":"https:\/\/doi.org\/10.1137\/15m1041754","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1]]}}}