{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:20:04Z","timestamp":1777443604722,"version":"3.51.4"},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2018,5,2]],"date-time":"2018-05-02T00:00:00Z","timestamp":1525219200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The following question was raised by Tuza in 1990 and Erd\u0151s et\u00a0al.\u00a0in 1992: if every edge of an <jats:italic>n<\/jats:italic>\u2010vertex chordal graph <jats:italic>G<\/jats:italic> is contained in a clique of size at least four, does <jats:italic>G<\/jats:italic> have a clique transversal, i.e.\u00a0a set of vertices meeting all nontrivial maximal cliques, of size at most <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/jgt22362-math-0001.png\" xlink:title=\"urn:x-wiley:03649024:media:jgt22362:jgt22362-math-0001\"\/>? We prove that every such graph <jats:italic>G<\/jats:italic> has a clique transversal of size at most <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/jgt22362-math-0002.png\" xlink:title=\"urn:x-wiley:03649024:media:jgt22362:jgt22362-math-0002\"\/> if <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/jgt22362-math-0003.png\" xlink:title=\"urn:x-wiley:03649024:media:jgt22362:jgt22362-math-0003\"\/>, which is the best possible bound.<\/jats:p>","DOI":"10.1002\/jgt.22362","type":"journal-article","created":{"date-parts":[[2018,5,3]],"date-time":"2018-05-03T07:36:33Z","timestamp":1525332993000},"page":"479-493","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimal\u2010size clique transversals in chordal graphs"],"prefix":"10.1002","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3049-6249","authenticated-orcid":false,"given":"Jacob W.","family":"Cooper","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics McGill University Burnside Hall Montreal QC H3A\u00a00B9 Canada"}]},{"given":"Andrzej","family":"Grzesik","sequence":"additional","affiliation":[{"name":"Department of Computer Science University of Warwick Coventry CV4 7AL UK"},{"name":"Faculty of Mathematics and Computer Science Jagiellonian University \u0141ojasiewicza 6 30\u2010348 Krak\u00f3w Poland"}]},{"given":"Daniel","family":"Kr\u00e1l'","sequence":"additional","affiliation":[{"name":"Mathematics Institute, DIMAP and Department of Computer Science University of Warwick Coventry CV4 7AL UK"}]}],"member":"311","published-online":{"date-parts":[[2018,5,2]]},"reference":[{"key":"e_1_2_6_2_1","unstructured":"M.AignerandT.Andreae Vertex\u2010sets that meet all maximal cliques of a graph Preprint 210 Fachbereich Mathematik FU Berlin 1986 14 pp."},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00087-9"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00276-O"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(92)90681-5"},{"key":"e_1_2_6_6_1","unstructured":"C.Flotow Obere Schranken f\u00fcr die Clique\u2010Transversalzahl eines Graphen Thesis Univ. 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LS\u201001\u20101 2001 30 pp."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.22362","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.22362","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,16]],"date-time":"2023-09-16T22:28:30Z","timestamp":1694903310000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.22362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,2]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["10.1002\/jgt.22362"],"URL":"https:\/\/doi.org\/10.1002\/jgt.22362","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,2]]},"assertion":[{"value":"2016-01-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-04-10","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-05-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}