{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:24:18Z","timestamp":1759335858832},"reference-count":12,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":11971,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1974,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A Proper graph G has no isolated points. Its Ramsey number r(G) is the minimum p such that every 2\u2010coloring of the edges of K<jats:sub>p<\/jats:sub> contains a monochromatic G. The Ramsey multiplicity R(G) is the minimum number of monochromatic G in any 2\u2010coloring of K<jats:sub>r(G)<\/jats:sub>. With just one exception, namely K<jats:sub>4<\/jats:sub>, we determine R(G) for proper graphs with at most 4 points. For the stars K<jats:sub>1,n<\/jats:sub>, it is shown that R = 2n when n is odd and R = 1 when n is even. We conclude with the conjecture that for a proper graph, R(G) = 1 if and only if G = K<jats:sub>2<\/jats:sub> or K<jats:sub>1,n<\/jats:sub> with n even.<\/jats:p>","DOI":"10.1002\/net.3230040206","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T01:27:04Z","timestamp":1178846824000},"page":"163-173","source":"Crossref","is-referenced-by-count":16,"title":["Generalized Ramsey theory for graphs IV, the Ramsey multiplicity of a graph"],"prefix":"10.1002","volume":"4","author":[{"given":"F.","family":"Harary","sequence":"first","affiliation":[]},{"given":"G.","family":"Prins","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02018466"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2037824"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"Chv\u00e1tal V.andF.Harary \u201cGeneralized Ramsey Theory for Graphs III Small Off\u2010Diagonal Numbers \u201dPacific J. Math. 1972.","DOI":"10.2140\/pjm.1972.41.335"},{"key":"e_1_2_1_5_2","first-page":"167","article-title":"On Ramsey\u2010Type Problems","volume":"10","author":"Gerencse\u00e9 L.","year":"1967","journal-title":"Ann. Univ. Sci. Budapest E\u00f6tv\u00f6s"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2310464"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1955-001-4"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2687868"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067364"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0067380"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.2307\/2317431"},{"key":"e_1_2_1_13_2","volume-title":"Graph Theory and Combinatorics","author":"Harary F.","year":"1974"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230040206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230040206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T14:19:18Z","timestamp":1699798758000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230040206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,1]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1974,1]]}},"alternative-id":["10.1002\/net.3230040206"],"URL":"https:\/\/doi.org\/10.1002\/net.3230040206","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1974,1]]}}}