{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:17Z","timestamp":1698385217643},"reference-count":5,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4176,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Consider a graph <jats:italic>G<\/jats:italic> with two distinguished sets of vertices: the <jats:italic>voters<\/jats:italic> and the <jats:italic>candidates.<\/jats:italic> A voter <jats:italic>v prefers<\/jats:italic> candidate <jats:italic>x<\/jats:italic> to candidate <jats:italic>y<\/jats:italic> if <jats:italic>d(v, x)<\/jats:italic> &lt; <jats:italic>d(v, y).<\/jats:italic> This preference relation defines an asymmetric digraph whose vertices are the candidates, in which there is an arc from candidate <jats:italic>x<\/jats:italic> to candidate <jats:italic>y<\/jats:italic> if and only if more voters prefer <jats:italic>x<\/jats:italic> to <jats:italic>y<\/jats:italic> than prefer <jats:italic>y<\/jats:italic> to <jats:italic>x.<\/jats:italic> T. W. Johnson and P. J. Slater (\u201cRealization of Majority Preference Digraphs by Graphically Determined Voting Patterns,\u201d <jats:italic>Congressus Numerantium<\/jats:italic>, vol. 67 [1988] 175\u2010186) have shown that each asymmetric digraph of order <jats:italic>n<\/jats:italic> can be <jats:italic>realized<\/jats:italic> in this way using a graph of order O(<jats:italic>n<\/jats:italic><jats:sup>2<\/jats:sup>). We present a new construction reducing the quadratic upper bound to a linear bound. \u00a9 1995 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190190309","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T13:54:19Z","timestamp":1180187659000},"page":"367-373","source":"Crossref","is-referenced-by-count":2,"title":["Realization of digraphs by preferences based on distances in graphs"],"prefix":"10.1002","volume":"19","author":[{"given":"Weizhen","family":"Gu","sequence":"first","affiliation":[]},{"given":"K. B.","family":"Reid","sequence":"additional","affiliation":[]},{"given":"Walter","family":"Schnyder","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"125","article-title":"On the representation of directed graphs as unions of orderings","volume":"9","author":"Erd\u00f6s P.","year":"1964","journal-title":"Magyar Tud. Akad. Mat. Kutat\u00f3 Int. K\u00f6zl."},{"key":"e_1_2_1_3_2","first-page":"175","article-title":"Realization of majority preference digraphs by graphically determined voting patterns","volume":"67","author":"Johnson T. W.","year":"1988","journal-title":"Congres. Numer."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/1907926"},{"key":"e_1_2_1_5_2","volume-title":"Topics on Tournaments","author":"Moon J. W.","year":"1968"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2310461"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190190309","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190190309","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T20:58:37Z","timestamp":1698353917000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190190309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/jgt.3190190309"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190190309","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}