{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T06:10:20Z","timestamp":1698127820073},"reference-count":4,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5605,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Wang and Williams defined a <jats:italic>threshold assignment<\/jats:italic> for a graph <jats:italic>G<\/jats:italic> as an assignment of a non\u2010negative weight to each vertex and edge of <jats:italic>G<\/jats:italic>, and a threshold <jats:italic>t<\/jats:italic>, such that a set <jats:italic>S<\/jats:italic> of vertices is stable if and only if the total weight of the subgraph induced by <jats:italic>S<\/jats:italic> does not exceed <jats:italic>t<\/jats:italic> \u2010 1. This is always possible with zero vertex\u2010weights, unit edge\u2010weights, and <jats:italic>t<\/jats:italic> = 1. By definition, a <jats:italic>threshold graph<\/jats:italic> is a graph having a threshold assignment with zero edge\u2010weights. The <jats:italic>threshold weight<\/jats:italic> of <jats:italic>G<\/jats:italic> is the minimum total edgeweight of a threshold assignment of <jats:italic>G.<\/jats:italic> A graph <jats:italic>G<\/jats:italic> = (<jats:italic>V,E<\/jats:italic>) is called <jats:italic>heavy<\/jats:italic> if its threshold weight is |<jats:italic>E<\/jats:italic>|. A clique <jats:italic>C<\/jats:italic> of <jats:italic>G<\/jats:italic> is called <jats:italic>big<\/jats:italic> if |<jats:italic>E<\/jats:italic>(<jats:italic>C<\/jats:italic>)| &gt; |<jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic> \u2010 <jats:italic>C<\/jats:italic>)|. Wang and Williams showed that graphs with a big clique are not heavy, and conjectured the converse. They verified the conjecture for triangle\u2010free graphs. We disprove the conjecture in general, but prove it for perfect graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190150203","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:48:42Z","timestamp":1181285322000},"page":"115-120","source":"Crossref","is-referenced-by-count":3,"title":["On a conjecture of wang and williams"],"prefix":"10.1002","volume":"15","author":[{"given":"N. V. R.","family":"Mahadev","sequence":"first","affiliation":[]},{"given":"Uri N.","family":"Peled","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(75)90041-6"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70731-3"},{"key":"e_1_2_1_4_2","unstructured":"C.Wang private communication."},{"key":"e_1_2_1_5_2","unstructured":"C.WangandA. C.Williams The threshold weight of a graph. RUTCOR Research Report RRR 32\u201389 Rutgers University New Brunswick NJ (1989) [J. Graph Theory forthcoming]."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150203","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T04:42:23Z","timestamp":1698036143000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,6]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1991,6]]}},"alternative-id":["10.1002\/jgt.3190150203"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150203","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,6]]}}}