{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:29:24Z","timestamp":1759847364402},"reference-count":17,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T00:00:00Z","timestamp":1159920000000},"content-version":"vor","delay-in-days":6882,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1987,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph is called \u201cperfectly orderable\u201d if its vertices can be ordered in such a way that, for each induced subgraph <jats:italic>F<\/jats:italic>, a certain \u201cgreedy\u201d coloring heuristic delivers an optimal coloring of <jats:italic>F<\/jats:italic>. No polynomial\u2010time algorithm to recognize these graphs is known. We present four classes of perfectly orderable graphs: Welsh\u2013Powell perfect graphs, Matula perfect graphs, graphs of Dilworth number at most three, and unions of two threshold graphs. Graphs in each of the first three classes are recognizable in a polynomial time. In every graph that belongs to one of the first two classes, we can find a largest clique and an optimal coloring in a linear time.<\/jats:p>","DOI":"10.1002\/jgt.3190110405","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T05:22:00Z","timestamp":1181366520000},"page":"481-495","source":"Crossref","is-referenced-by-count":60,"title":["Four classes of perfectly orderable graphs"],"prefix":"10.1002","volume":"11","author":[{"given":"V.","family":"Chv\u00e1tal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C. T.","family":"Ho\u00e0ng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. V. R.","family":"Mahadev","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"De Werra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,4]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Topics on Perfect Graphs","author":"Berge C.","year":"1984"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72922-0"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72923-2"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70731-3"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/1969503"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70334-0"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(84)90016-7"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0606049"},{"key":"e_1_2_1_10_2","first-page":"481","article-title":"A min\u2010max theorem with application to graph coloring","volume":"10","author":"Matula D. W.","year":"1968","journal-title":"SIAM Rev."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1137\/0122040"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/2402.322385"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(76)80008-8"},{"key":"e_1_2_1_14_2","unstructured":"M.Preissmann A class of strongly perfect graphs. Technical Report ORWP \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (1983)."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(82)90068-5"},{"key":"e_1_2_1_16_2","volume-title":"Discrete Optimization Algorithms","author":"Systo M. M.","year":"1983"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(68)80081-X"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/10.1.85"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190110405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190110405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T09:35:13Z","timestamp":1697880913000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190110405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1987,12]]}},"alternative-id":["10.1002\/jgt.3190110405"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190110405","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,12]]}}}