{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T05:09:35Z","timestamp":1723093775361},"reference-count":5,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T00:00:00Z","timestamp":1172102400000},"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":[[2007,7]]},"abstract":"Abstract<\/jats:title>The second neighborhood conjecture of Seymour asserts that for any orientation G<\/jats:italic> = (V<\/jats:italic>,E<\/jats:italic>), there exists a vertex \u03c5 \u2208 V<\/jats:italic> so that |N<\/jats:italic>+<\/jats:sup>(\u03c5)| \u2264 |N<\/jats:italic>++<\/jats:sup>(\u03c5)|. The conjecture was resolved by Fisher for tournaments. In this article, we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results, and reduce an asymptotic version of the conjecture to a finite case. \u00a9 2007 Wiley Periodicals, Inc. J Graph Theory 55: 208\u2013220, 2007<\/jats:p>","DOI":"10.1002\/jgt.20229","type":"journal-article","created":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T20:39:02Z","timestamp":1172176742000},"page":"208-220","source":"Crossref","is-referenced-by-count":19,"title":["Remarks on the second neighborhood problem"],"prefix":"10.1002","volume":"55","author":[{"given":"D.","family":"Fidler","sequence":"first","affiliation":[]},{"given":"R.","family":"Yuster","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,2,22]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"73","article-title":"Squaring the tournament: an open problem","volume":"109","author":"Dean N.","year":"1995","journal-title":"Congressus Numerantium"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199609)23:1<43::AID-JGT4>3.0.CO;2-K"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s000260300001"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/1097-0118(200012)35:4<244::AID-JGT2>3.0.CO;2-H"},{"key":"e_1_2_1_6_2","first-page":"201","article-title":"The minimum degree approach for Paul Seymour's distance 2 conjecture","volume":"148","author":"Kaneko Y.","year":"2001","journal-title":"Congressus Numerantium"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20229","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20229","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T19:15:35Z","timestamp":1697656535000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20229"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,22]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,7]]}},"alternative-id":["10.1002\/jgt.20229"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20229","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,22]]}}}