{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:47:30Z","timestamp":1759063650170},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T00:00:00Z","timestamp":1159920000000},"content-version":"vor","delay-in-days":7157,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1987,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Galeana\u2010Sanchez and Neumann\u2010Lara proved that a sufficient condition for a digraph to have a kernel (i.e., an absorbent independent set) is the following: (P) every odd directed cycle possesses at least two directed chords whose terminal endpoints are consecutive on the cycle. Here it is proved that (P) is satisfied by those digraphs having these two properties: (i) the reversal of every 3\u2010circuit is present, and (ii) every odd directed cycle <jats:italic>v<\/jats:italic><jats:sub>1<\/jats:sub>\u2026 <jats:italic>v<\/jats:italic><jats:sub>2<jats:italic>n<\/jats:italic>+1<\/jats:sub> <jats:italic>V<\/jats:italic><jats:sub>1<\/jats:sub> has two chords of the form (<jats:italic>v<\/jats:italic><jats:sub>i<\/jats:sub>, v<jats:sub>i+2<\/jats:sub>). This is stronger than a result of Galeana\u2010Sanchez.<\/jats:p>","DOI":"10.1002\/jgt.3190110112","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T08:56:30Z","timestamp":1180428990000},"page":"81-85","source":"Crossref","is-referenced-by-count":14,"title":["A sufficient condition for a digraph to be kernel\u2010perfect"],"prefix":"10.1002","volume":"11","author":[{"given":"P.","family":"Duchet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,4]]},"reference":[{"key":"e_1_2_1_2_2","author":"Berge C.","journal-title":"Discrete Math."},{"key":"e_1_2_1_3_2","unstructured":"M.Blidia P.Duchet andF.Maffray On orientations of perfect graphs in preparation."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70041-4"},{"key":"e_1_2_1_5_2","article-title":"Parity graphs are kernel M\u2010solvable","author":"Duchet P.","journal-title":"J. Combinat. Theory B"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90017-1"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90087-5"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(84)90131-6"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/1969755"},{"key":"e_1_2_1_10_2","volume-title":"Theory of Games and Economic Behavior","author":"Von Neumann J.","year":"1944"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190110112","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190110112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T14:36:26Z","timestamp":1697898986000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190110112"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1987,3]]}},"alternative-id":["10.1002\/jgt.3190110112"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190110112","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,3]]}}}