{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:39:21Z","timestamp":1774625961742,"version":"3.50.1"},"reference-count":12,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4357,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph is well covered if every maximal independent set has the same cardinality. A vertex <jats:italic>x<\/jats:italic>, in a well\u2010covered graph <jats:italic>G<\/jats:italic>, is called extendable if <jats:italic>G \u2013 {x}<\/jats:italic> is well covered and \u03b2(<jats:italic>G<\/jats:italic>) = \u03b2(<jats:italic>G \u2013 {x}<\/jats:italic>). If <jats:italic>G<\/jats:italic> is a connected, well\u2010covered graph containing no 4\u2010 nor 5\u2010cycles as subgraphs and <jats:italic>G<\/jats:italic> contains an extendable vertex, then <jats:italic>G<\/jats:italic> is the disjoint union of edges and triangles together with a restricted set of edges joining extendable vertices. There are only 3 other connected, well\u2010covered graphs of this type that do not contain an extendable vertex. Moreover, all these graphs can be recognized in polynomial time.<\/jats:p>","DOI":"10.1002\/jgt.3190180707","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T16:19:58Z","timestamp":1181233198000},"page":"713-721","source":"Crossref","is-referenced-by-count":43,"title":["A characterization of well\u2010covered graphs that contain neither 4\u2010 nor 5\u2010cycles"],"prefix":"10.1002","volume":"18","author":[{"given":"A.","family":"Finbow","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Hartnell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. J.","family":"Nowakowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"C.Berge Some common properties for regularizable graphs edge\u2010critical graphs and B\u2010graphs.Tohoku University Tsuken Symposium on Graph Theory and Algorithms Oct1980 108\u2013123.","DOI":"10.1007\/3-540-10704-5_10"},{"key":"e_1_2_1_3_2","unstructured":"S. R.Campbell Some results on cubic well\u2010covered graphs. Ph.D. dissertation Vanderbilt University (1987)."},{"key":"e_1_2_1_4_2","first-page":"215","article-title":"On well\u2010covered, 3\u2010polytopes","volume":"25","author":"Campbell S. R.","year":"1988","journal-title":"Ars Combinat."},{"key":"e_1_2_1_5_2","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90215-1"},{"key":"e_1_2_1_7_2","first-page":"189","article-title":"A game related to covering by stars","volume":"16","author":"Finbow A.","year":"1983","journal-title":"Ars Combinat."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1993.1005"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80011-4"},{"key":"e_1_2_1_10_2","first-page":"20","article-title":"Well covered graphs","volume":"2","author":"Ravindra G.","year":"1977","journal-title":"J. Combin. Inform. System. Sci."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230220304"},{"key":"e_1_2_1_12_2","unstructured":"J. A.Staples On some subclasses of well\u2010covered graphs. Ph.D. dissertation Vanderbilt University (1975)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190030211"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180707","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180707","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T17:48:40Z","timestamp":1698169720000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180707"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,11]]},"references-count":12,"journal-issue":{"issue":"7","published-print":{"date-parts":[[1994,11]]}},"alternative-id":["10.1002\/jgt.3190180707"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180707","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,11]]}}}