{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:31Z","timestamp":1740155971133,"version":"3.37.3"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> The [Formula: see text]-chordal graphs, defined by no induced cycle having length greater than [Formula: see text], generalize the traditional chordal graphs (where [Formula: see text]), which Dirac characterized in 1961 by minimal separators always inducing complete subgraphs. The more recent unichord-free graphs, defined by no cycle having a unique chord, have been characterized by minimal separators always inducing edgeless subgraphs. This sharp contrast of minimal separators motivates a new concept of [Formula: see text]-unichord-free graphs, strengthening the unichord-free graphs (where [Formula: see text]). The class of all unichord-free graphs decomposes into subclasses that are simultaneously [Formula: see text]-chordal and [Formula: see text]-unichord-free, leading to characterizations of some of these subclasses and to open questions about their overall structure as [Formula: see text] and [Formula: see text] increase. <\/jats:p>","DOI":"10.1142\/s179383091850043x","type":"journal-article","created":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T02:56:06Z","timestamp":1522205766000},"page":"1850043","source":"Crossref","is-referenced-by-count":0,"title":["Characterizing k-chordal unichord-free graphs"],"prefix":"10.1142","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0745-6716","authenticated-orcid":false,"given":"Terry A.","family":"McKee","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Statistics, Wright State University, Dayton, Ohio 45435, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,7,30]]},"reference":[{"doi-asserted-by":"publisher","key":"S179383091850043XBIB001","DOI":"10.1016\/0095-8956(86)90043-2"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB002","DOI":"10.1137\/1.9780898719796"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB003","DOI":"10.1016\/S0012-365X(01)00166-2"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB004","DOI":"10.1007\/BF02992776"},{"key":"S179383091850043XBIB005","first-page":"113","volume-title":"Perfect Graphs","author":"Hayward R.","year":"2001"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB006","DOI":"10.1016\/j.disc.2013.08.032"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB007","DOI":"10.1016\/j.dam.2011.03.024"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB008","DOI":"10.1016\/j.disc.2013.03.020"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB009","DOI":"10.1016\/j.dam.2012.02.016"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB010","DOI":"10.1016\/j.tcs.2009.12.018"},{"key":"S179383091850043XBIB011","first-page":"217","volume":"73","author":"McKee T. A.","year":"2007","journal-title":"Util. Math."},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB012","DOI":"10.7151\/dmgt.1831"},{"doi-asserted-by":"publisher","key":"S179383091850043XBIB013","DOI":"10.1002\/jgt.20405"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091850043X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T08:44:35Z","timestamp":1565081075000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091850043X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,30]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2018,7,30]]},"published-print":{"date-parts":[[2018,8]]}},"alternative-id":["10.1142\/S179383091850043X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091850043x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2018,7,30]]}}}