{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T08:45:20Z","timestamp":1751877920076},"reference-count":13,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4084,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The following definition is motivated by the study of circle orders and their connections to graphs. A graphs <jats:italic>G<\/jats:italic> is called a <jats:italic>point\u2010halfspace graph<\/jats:italic> (in <jats:bold>R<\/jats:bold><jats:sup>k<\/jats:sup>) provided one can assign to each vertex <jats:italic>v<\/jats:italic> \u03f5 (<jats:italic>G<\/jats:italic>) a point <jats:bold>p<\/jats:bold><jats:sub>v<\/jats:sub> <jats:bold>R<\/jats:bold><jats:sup>k<\/jats:sup> and to each edge <jats:italic>e<\/jats:italic> \u03f5 <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) a closed halfspace <jats:italic>H<\/jats:italic><jats:sub>e<\/jats:sub> \u03f5 <jats:bold>R<\/jats:bold><jats:sup>k<\/jats:sup> so that <jats:italic>v<\/jats:italic> is incident with <jats:italic>e<\/jats:italic> if and only if <jats:bold>p<\/jats:bold><jats:sub>v<\/jats:sub> \u03f5 <jats:italic>H<\/jats:italic><jats:sub>e<\/jats:sub>. Let <jats:bold>H<\/jats:bold><jats:sup>k<\/jats:sup> denote the set of point\u2010halfspace graphs (in <jats:bold>R<\/jats:bold><jats:sup>k<\/jats:sup>).<\/jats:p><jats:p>We give complete forbidden subgraph and structural characterizations of the classes <jats:bold>H<\/jats:bold><jats:sup>k<\/jats:sup> for every <jats:italic>k<\/jats:italic>. Surprisingly, these classes are closed under taking minors and we give forbidden minor characterizations as well. \u00a9 1996 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190200103","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T15:24:58Z","timestamp":1181229898000},"page":"19-35","source":"Crossref","is-referenced-by-count":1,"title":["On point\u2010halfspace graphs"],"prefix":"10.1002","volume":"20","author":[{"given":"Edward R.","family":"Scheinerman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ann N.","family":"Trenk","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Ullman","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":"publisher","DOI":"10.1007\/BFb0060102"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/0406017"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00563524"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"D.Gale Neighborly and cyclic polygotes inConvexity Proceedings of the AMS Symposium in Pure Mathematics Vol. VII (1963)225\u2013232.","DOI":"10.1090\/pspum\/007\/0152944"},{"key":"e_1_2_1_6_2","volume-title":"Convex Polytopes","author":"Gr\u00fcnbaum B.","year":"1967"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00354890"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01464231"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0404040"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190170303"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00714474"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00353652"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00143891"},{"key":"e_1_2_1_14_2","first-page":"1","article-title":"Polyeder und Raumeinteilungen","volume":"3","author":"Steinitz E.","year":"1992","journal-title":"Enzykl. 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Wiss."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190200103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190200103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:18:53Z","timestamp":1698351533000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190200103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,8]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,8]]}},"alternative-id":["10.1002\/jgt.3190200103"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190200103","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,8]]}}}