{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:08:22Z","timestamp":1699834102430},"reference-count":7,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":10259,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1978,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The number of vertices in a digraph <jats:italic>G<\/jats:italic> having a particular outdegree (indegree) is called the <jats:italic>frequency<\/jats:italic> of the outdegree (indegree). A set <jats:italic>F<\/jats:italic> of distinct positive integers {<jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>2<\/jats:sub>, \u2026, <jats:italic>f<jats:sub>n<\/jats:sub><\/jats:italic>} is the frequency set of the digraph <jats:italic>G<\/jats:italic> if every outdegree and indegree occurs with frequency <jats:italic>f<jats:sub>j<\/jats:sub><\/jats:italic>\u2208<jats:italic>F<\/jats:italic> and for each <jats:italic>f<jats:sub>j<\/jats:sub><\/jats:italic>\u2208<jats:italic>F<\/jats:italic> there is a least one outdegree and at least one indegree with frequency <jats:italic>f<jats:sub>j<\/jats:sub><\/jats:italic>. We prove that each nonempty set <jats:italic>F<\/jats:italic> of positive integers is the frequency set of some tournament, and we determine the smallest possible order for such a tournament. Similar results for asymmetric digraphs are also given. The results and techniques for frequency sets are used to derive corresponding results for vertex frequency partitions.<\/jats:p>","DOI":"10.1002\/jgt.3190020307","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:15:16Z","timestamp":1180419316000},"page":"241-249","source":"Crossref","is-referenced-by-count":4,"title":["Degree frequencies in digraphs and tournaments"],"prefix":"10.1002","volume":"2","author":[{"given":"Brian","family":"Alspach","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K. B.","family":"Reid","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02019997"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059424"},{"key":"e_1_2_1_4_2","volume-title":"Structural Models: An Introduction to the Theory of Directed Graphs","author":"Harary F.","year":"1965"},{"key":"e_1_2_1_5_2","first-page":"419","volume-title":"Proceedings of the Eighth Southeastern Conference on Combinatorics, Graph Theory, and Computing","author":"Johnson R. H.","year":"1977"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4064\/fm-95-3-189-194"},{"key":"e_1_2_1_7_2","series-title":"Athena Series","volume-title":"Topics on Tournaments","author":"Moon J. W.","year":"1968"},{"key":"e_1_2_1_8_2","article-title":"Score sets for tournaments. Proceedings of the Ninth Southeastern Conference on Combinatorics, Graph Theory, and Computing","author":"Reid K. B.","journal-title":"Utilitas Mathematica, Winnipeg"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190020307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190020307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:01:24Z","timestamp":1699786884000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190020307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1978,9]]}},"alternative-id":["10.1002\/jgt.3190020307"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190020307","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,9]]}}}