{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T06:40:58Z","timestamp":1698043258176},"reference-count":4,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":5788,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1990,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For any graph <jats:italic>G<\/jats:italic>, let <jats:italic>i<\/jats:italic>(<jats:italic>G<\/jats:italic>) and \u03bc;(<jats:italic>G<\/jats:italic>) denote the smallest number of vertices in a maximal independent set and maximal clique, respectively. For positive integers <jats:italic>m<\/jats:italic> and <jats:italic>n<\/jats:italic>, the lower Ramsey number <jats:italic>s<\/jats:italic>(<jats:italic>m, n<\/jats:italic>) is the largest integer <jats:italic>p<\/jats:italic> so that every graph of order <jats:italic>p<\/jats:italic> has <jats:italic>i<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2264 <jats:italic>m<\/jats:italic> or \u03bc;(<jats:italic>G<\/jats:italic>) \u2264 <jats:italic>n<\/jats:italic>. In this paper we give several new lower bounds for <jats:italic>s<\/jats:italic> (<jats:italic>m, n<\/jats:italic>) as well as determine precisely the values <jats:italic>s<\/jats:italic>(1, <jats:italic>n<\/jats:italic>).<\/jats:p>","DOI":"10.1002\/jgt.3190140612","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:50:25Z","timestamp":1181285425000},"page":"723-730","source":"Crossref","is-referenced-by-count":0,"title":["Lower bounds for lower Ramsey numbers"],"prefix":"10.1002","volume":"14","author":[{"given":"Ralph","family":"Faudree","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronald J.","family":"Gould","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael S.","family":"Jacobson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linda","family":"Lesniak","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","unstructured":"C.Berge Graphs and Hypergraphs.North\u2010Holland Amsterdam (1973)."},{"key":"e_1_2_1_3_2","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"e_1_2_1_4_2","article-title":"Generalised maximal independence and clique numbers of graphs","author":"Mynhardt C. M.","journal-title":"Quaestiones Mathematica"},{"key":"e_1_2_1_5_2","unstructured":"C. M.Mynhardt On a Ramsey type problem for independent domination parameters of graphs. Preprint."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190140612","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190140612","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T18:32:30Z","timestamp":1697999550000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190140612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,12]]},"references-count":4,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1990,12]]}},"alternative-id":["10.1002\/jgt.3190140612"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190140612","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,12]]}}}