{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:08:28Z","timestamp":1699834108892},"reference-count":6,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8890,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>t<\/jats:italic>(<jats:italic>n<\/jats:italic>) denote the greatest number of arcs in a diagraph of orders <jats:italic>n<\/jats:italic> which does not contain any antidrected cycles. We show that [16\/5(<jats:italic>n<\/jats:italic> \u2212 1)] \u2264 <jats:italic>t<\/jats:italic>(<jats:italic>n<\/jats:italic>) \u2264 1\/2 (<jats:italic>n<\/jats:italic> \u2212 1) for n \u2265 5. Let <jats:italic>t<jats:sub>r<\/jats:sub><\/jats:italic> (<jats:italic>n<\/jats:italic>) denote the corresponding quantity for <jats:italic>r<\/jats:italic>\u2010colorable digraphs. We show that [16\/5(<jats:italic>n<\/jats:italic> \u2212 1)] \u2264 <jats:italic>t<\/jats:italic><jats:sub>5<\/jats:sub>(<jats:italic>n<\/jats:italic>) \u2264 <jats:italic>t<\/jats:italic><jats:sub>6<\/jats:sub>(<jats:italic>n<\/jats:italic>) \u2264 10\/3(<jats:italic>n<\/jats:italic> \u2212 1) for <jats:italic>n<\/jats:italic> \u2265 5 and that <jats:italic>t<\/jats:italic><jats:sub>4<\/jats:sub>(<jats:italic>n<\/jats:italic>) = 3(<jats:italic>n<\/jats:italic> \u2212 1) for <jats:italic>n<\/jats:italic> \u2265 3.<\/jats:p>","DOI":"10.1002\/jgt.3190060207","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:47:37Z","timestamp":1180421257000},"page":"133-138","source":"Crossref","is-referenced-by-count":1,"title":["On digraphs without antidirected cycles"],"prefix":"10.1002","volume":"6","author":[{"given":"Douglas D.","family":"Grant","sequence":"first","affiliation":[]},{"given":"F.","family":"Jaeger","sequence":"additional","affiliation":[]},{"given":"C.","family":"Payan","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Extremal k\u2010colorable Subgraphs","author":"Andersen L.","journal-title":"Ars Combinatoria."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2"},{"key":"e_1_2_1_4_2","unstructured":"D. D.Grant Some Problems in Graph Theory. Ph.D. Thesis University of Reading (1979)."},{"key":"e_1_2_1_5_2","unstructured":"F.JaegerandC.Payan On Graphs Without Anti\u2010directed Cycles and Related Topics. Research Report No. 135 Laboratoire d'Informatique et Math\u00e9matiques Appliqu\u00e9s de Grenoble."},{"key":"e_1_2_1_6_2","unstructured":"J.Lehel Counterexample for H\u00e4ggkvist's Conjecture.Graph Theory Newsl.(1979)."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(68)80081-X"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060207","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060207","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:21:35Z","timestamp":1699766495000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060207"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["10.1002\/jgt.3190060207"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060207","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}