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While many distinct tournaments may have the same score sequence, there exist score sequences such that any tournament with score sequence has an embedding with no nonsplit consistently oriented link. We call such score sequences linkless<\/jats:italic>, and we show that the vast majority of score sequences for 8 vertex tournaments are linkless. We also extend these results to vertex tournaments and are able to classify many longer score sequences as well. We show that for any , there exist at least linkless score sequences, but we conjecture that the fraction of score sequences of length that are linkless goes to 0 as becomes large.<\/jats:p>","DOI":"10.1002\/jgt.22753","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T23:13:26Z","timestamp":1633734806000},"page":"573-593","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Classifying intrinsically linked tournaments by score sequence"],"prefix":"10.1002","volume":"99","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-2947-4587","authenticated-orcid":false,"given":"Thomas","family":"Fleming","sequence":"first","affiliation":[{"name":"Department of Mathematics SUNY Potsdam Potsdam New York USA"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-1584-4973","authenticated-orcid":false,"given":"Joel","family":"Foisy","sequence":"additional","affiliation":[{"name":"Department of Mathematics SUNY Potsdam Potsdam New York USA"}]}],"member":"311","published-online":{"date-parts":[[2021,10,7]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216504003421"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190070410"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216518500372"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218216519500767"},{"key":"e_1_2_6_6_1","first-page":"173","article-title":"Counting links in complete graphs","volume":"46","author":"Fleming T.","year":"2009","journal-title":"Osaka J. Math."},{"key":"e_1_2_6_7_1","first-page":"817","article-title":"Intrinsic linking in directed graphs","volume":"52","author":"Foisy J.","year":"2015","journal-title":"Osaka J. Math."},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1999.3054"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02476378"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01364272"},{"key":"e_1_2_6_11_1","unstructured":"T.Mattman R.Naimi andB.Pagano Intrinsic linking and knotting are arbitrarily complex in directed graphs arXiv:1901.01212."},{"issue":"4","key":"e_1_2_6_12_1","first-page":"655","article-title":"A note on spatial representation of graphs","volume":"26","author":"Ne\u0161et\u0159il J.","year":"1985","journal-title":"Commentat. Math. Univ. 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