{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T05:18:32Z","timestamp":1768627112171,"version":"3.49.0"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T00:00:00Z","timestamp":1616457600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this short note we prove that every tournament contains the <jats:italic>k<\/jats:italic>-th power of a directed path of linear length. This improves upon recent results of Yuster and of Gir\u00e3o. We also give a complete solution for this problem when <jats:italic>k<\/jats:italic>=2, showing that there is always a square of a directed path of length <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548321000067_inline1.png\"\/>, which is best possible.<\/jats:p>","DOI":"10.1017\/s0963548321000067","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T07:28:32Z","timestamp":1616484512000},"page":"894-898","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":8,"title":["Powers of paths in tournaments"],"prefix":"10.1017","volume":"30","author":[{"given":"Nemanja","family":"Dragani\u0107","sequence":"first","affiliation":[]},{"given":"Fran\u00e7ois","family":"Dross","sequence":"additional","affiliation":[]},{"given":"Jacob","family":"Fox","sequence":"additional","affiliation":[]},{"given":"Ant\u00f3nio","family":"Gir\u00e3o","sequence":"additional","affiliation":[]},{"given":"Fr\u00e9d\u00e9ric","family":"Havet","sequence":"additional","affiliation":[]},{"given":"D\u00e1niel","family":"Kor\u00e1ndi","sequence":"additional","affiliation":[]},{"given":"William","family":"Lochet","sequence":"additional","affiliation":[]},{"given":"David Munh\u00e1","family":"Correia","sequence":"additional","affiliation":[]},{"given":"Alex","family":"Scott","sequence":"additional","affiliation":[]},{"given":"Benny","family":"Sudakov","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,23]]},"reference":[{"key":"S0963548321000067_ref4","unstructured":"[4] Gir\u00e3o, A. , A note on long powers of paths in tournaments, arXiv:2010.02875 preprint."},{"key":"S0963548321000067_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01626028"},{"key":"S0963548321000067_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(90)90085-E"},{"key":"S0963548321000067_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2020.112168"},{"key":"S0963548321000067_ref6","volume-title":"Introduction to Graph Theory","author":"West","year":"2001"},{"key":"S0963548321000067_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02024498"},{"key":"S0963548321000067_ref2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.69"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548321000067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,15]],"date-time":"2021-10-15T15:51:34Z","timestamp":1634313094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548321000067\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,23]]},"references-count":7,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["S0963548321000067"],"URL":"https:\/\/doi.org\/10.1017\/s0963548321000067","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,23]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}