{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T20:59:25Z","timestamp":1772571565149,"version":"3.50.1"},"reference-count":4,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":4966,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1993,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>ex<\/jats:italic> * (<jats:italic>D<\/jats:italic>; <jats:italic>H<\/jats:italic>) denote the maximum number of edges in a connected graph with maximum degree <jats:italic>D<\/jats:italic> and no induced subgraph isomorphic to <jats:italic>H.<\/jats:italic> We prove that this is finite only when <jats:italic>H<\/jats:italic> is a disjoint union of paths,m in which case we provide crude upper and lower bounds. When <jats:italic>H<\/jats:italic> is the four\u2010vertex path <jats:italic>P<\/jats:italic><jats:sub>4<\/jats:sub>, we prove that the complete bipartite graph <jats:italic>K<\/jats:italic><jats:sub><jats:italic>D,D<\/jats:italic><\/jats:sub> is the unique extremal graph. Furthermore, if <jats:italic>G<\/jats:italic> is a connected <jats:italic>P<\/jats:italic><jats:sub>4<\/jats:sub>\u2010free graph with maximum degree <jats:italic>D<\/jats:italic> and clique number \u03c9, then <jats:italic>G<\/jats:italic> has at most <jats:italic>D<\/jats:italic><jats:sup>2<\/jats:sup> \u2212 <jats:italic>D<\/jats:italic>(\u03c9 \u2212 2)\/2 edges. \u00a9 1993 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190170111","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T22:17:42Z","timestamp":1181254662000},"page":"109-116","source":"Crossref","is-referenced-by-count":3,"title":["Large <i>P<\/i><sub>4<\/sub>\u2010free graphs with bounded degree"],"prefix":"10.1002","volume":"17","author":[{"given":"Myung S.","family":"Chung","sequence":"first","affiliation":[]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"292","volume-title":"Extremal Graph Theory","author":"Bollob\u00e1s B.","year":"1978"},{"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","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(90)90144-7"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90063-X"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190170111","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190170111","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T08:54:20Z","timestamp":1698224060000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190170111"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,3]]},"references-count":4,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1993,3]]}},"alternative-id":["10.1002\/jgt.3190170111"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190170111","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,3]]}}}