{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T11:17:39Z","timestamp":1763551059454},"reference-count":2,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5878,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In a connected graph define the k\u2010center as the set of vertices whose distance from any other vertex is at most <jats:italic>k.<\/jats:italic> We say that a vertex set <jats:italic>S<\/jats:italic> <jats:italic>d<\/jats:italic>\u2010dominates <jats:italic>G<\/jats:italic> if for every vertex x there is a y \u2208 <jats:italic>S<\/jats:italic> whose distance from <jats:italic>x<\/jats:italic> is at most <jats:italic>d<\/jats:italic>.<\/jats:p><jats:p>Call a graph <jats:italic>P<jats:sub>t<\/jats:sub><\/jats:italic>\u2010free if it does not contain a path on <jats:italic>t<\/jats:italic> vertices as an induced subgraph. We prove that a connected graph is <jats:italic>P<jats:sub>2k\u20101<\/jats:sub><\/jats:italic>\u2010free (<jats:italic>P<jats:sub>2k<\/jats:sub><\/jats:italic>\u2010free) if and only if each of its connected induced subgraphs <jats:italic>H<\/jats:italic> satisfy the following property: The <jats:italic>k<\/jats:italic>\u2010center of <jats:italic>H<\/jats:italic> (<jats:italic>k<\/jats:italic> \u2010 1)\u2010dominates ((<jats:italic>k<\/jats:italic> \u2010 2)\u2010dominates) <jats:italic>H<\/jats:italic>.<\/jats:p><jats:p>Moreover, we show that the subgraph induced by the (<jats:italic>t<\/jats:italic> \u2010 3)\u2010center in any <jats:italic>P<jats:sub>t<\/jats:sub><\/jats:italic>\u2010free connected graph is again connected and has diameter at most <jats:italic>t<\/jats:italic> \u2010 3.<\/jats:p>","DOI":"10.1002\/jgt.3190140409","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T12:52:36Z","timestamp":1180183956000},"page":"455-464","source":"Crossref","is-referenced-by-count":28,"title":["A characterization of graphs without long induced paths"],"prefix":"10.1002","volume":"14","author":[{"given":"G\u00e1bor","family":"Bacs\u00f3","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zsolt","family":"Tuza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"Dominating cliques in P5\u2010free graphs","author":"Bacs\u00f3 G.","journal-title":"Periodica Math. Hungar."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(86)90028-6"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190140409","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140409","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:36:26Z","timestamp":1698042986000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,9]]},"references-count":2,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1990,9]]}},"alternative-id":["10.1002\/jgt.3190140409"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140409","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,9]]}}}