{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T18:45:45Z","timestamp":1700160345942},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2003,11,25]],"date-time":"2003-11-25T00:00:00Z","timestamp":1069718400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2004,1]]},"abstract":"Abstract<\/jats:title>A feedback arc set of a digraph is a set of arcs whose reversal makes the resulting digraph acyclic. Given a tournament with a disjoint union of directed paths as a feedback arc set, we present necessary and sufficient conditions for this feedback arc set to have minimum size. We will present a construction for tournaments where the difference between the size of a minimum feedback arc set and the size of the largest collection of arc disjoint cycles can be made arbitrarily large. We will also make a connection to a problem found in [Barth\u00e9lemy et al., 2<\/jats:ext-link>]. The reversing number of a digraph was defined to be $r(D)\\, = |V(T)|-|V(D)|$<\/jats:styled-content> where T<\/jats:italic> is a smallest tournament having the arc set of D<\/jats:italic> as a minimum feedback arc set. As a consequence of our classification of all tournaments having a disjoint union of directed paths as a minimum feedback arc set, we will obtain a new result involving the reversing number. We obtain precise reversing numbers for all digraphs consisting of a disjoint union of directed paths. \u00a9 2003 Wiley Periodicals, Inc. J Graph Theory 45: 28\u201347, 2004<\/jats:p>","DOI":"10.1002\/jgt.10155","type":"journal-article","created":{"date-parts":[[2003,12,2]],"date-time":"2003-12-02T14:26:46Z","timestamp":1070375206000},"page":"28-47","source":"Crossref","is-referenced-by-count":2,"title":["Complete classification of tournaments having a disjoint union of directed paths as a minimum feedback arc set"],"prefix":"10.1002","volume":"45","author":[{"given":"Garth","family":"Isaak","sequence":"first","affiliation":[]},{"given":"Darren A.","family":"Narayan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2003,12,15]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"51","article-title":"Tournaments with a transitive subtournament as a feedback arc set","volume":"158","author":"Baldwin J. L.","year":"2002","journal-title":"Congr Numer"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)00042-C"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1965-017-1"},{"key":"e_1_2_1_5_2","first-page":"1","article-title":"Tournaments as feedback arc sets","volume":"20","author":"Isaak G.","year":"1995","journal-title":"Electron J Combin"},{"key":"e_1_2_1_6_2","article-title":"Tournaments with feedback path powers","author":"Narayan D. A.","journal-title":"Journal of Combinatorial Mathematics and Combinatorial Computing"},{"key":"e_1_2_1_7_2","first-page":"53","article-title":"The reversing number of a digraph; A disjoint union of directed stars","volume":"145","author":"Narayan D. A.","year":"2000","journal-title":"Congr Numer"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/48.3-4.303"},{"key":"e_1_2_1_9_2","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1963.1082116"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.10155","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.10155","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T18:09:43Z","timestamp":1700158183000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.10155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12,15]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1002\/jgt.10155"],"URL":"https:\/\/doi.org\/10.1002\/jgt.10155","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12,15]]}}}