{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T08:28:30Z","timestamp":1698654510249},"reference-count":15,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":5397,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Say a graph H <jats:italic>selects<\/jats:italic> a graph <jats:italic>G<\/jats:italic> if given any coloring of <jats:italic>H<\/jats:italic>, there will be a monochromatic induced copy of <jats:italic>G<\/jats:italic> in <jats:italic>H<\/jats:italic> or a completely multicolored copy of <jats:italic>G<\/jats:italic> in <jats:italic>H<\/jats:italic>. Denote by <jats:italic>s(G)<\/jats:italic> the minimum order of a graph that selects <jats:italic>G<\/jats:italic> and set <jats:italic>s(n)<\/jats:italic> = max {<jats:italic>s(G)<\/jats:italic>: |G| = <jats:italic>n<\/jats:italic>}. Upper and lower bounds are given for this function. Also, consider the Folkman function <jats:italic>f<jats:sub>r<\/jats:sub>(n)<\/jats:italic> = max{min{|<jats:italic>V(H<\/jats:italic>)|: <jats:italic>H<\/jats:italic> \u2192 (<jats:italic>G<\/jats:italic>)<jats:sup>1<\/jats:sup><jats:sub>r<\/jats:sub>}: |<jats:italic>V(G)<\/jats:italic>| = <jats:italic>n<\/jats:italic>}, where <jats:italic>H<\/jats:italic> \u2192 (<jats:italic>G<\/jats:italic>)<jats:sup>1<\/jats:sup><jats:sub>r<\/jats:sub> indicates that <jats:italic>H<\/jats:italic> is vertex Ramsey to <jats:italic>G<\/jats:italic>, that is, any vertex coloring of <jats:italic>H<\/jats:italic> with <jats:italic>r<\/jats:italic> colors admits a monochromatic induced copy of <jats:italic>G<\/jats:italic>. The method used provides a better upper bound for this function than was previously known. As a tool, we establish a theorem for projective planes.<\/jats:p>","DOI":"10.1002\/rsa.3240030406","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T18:21:06Z","timestamp":1180203666000},"page":"427-444","source":"Crossref","is-referenced-by-count":7,"title":["A Canonical Ramsey Theorem"],"prefix":"10.1002","volume":"3","author":[{"given":"Nancy","family":"Eaton","sequence":"first","affiliation":[]},{"given":"Vojt\u011bch","family":"R\u00f6dl","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"583","volume-title":"Graph Theory With Applications to Algorithms and Computer Science","author":"Broere I.","year":"1985"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190110113"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(91)90089-3"},{"key":"e_1_2_1_5_2","volume-title":"Linear Programming","author":"Chv\u00e1tal V.","year":"1983"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1972-063-2"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/B978-0-444-86893-0.50020-6","volume-title":"Colloquia Mathematical Societatis Janos Bolyai 37 Finite and Infinite Sets","author":"Erd\u00f6s P.","year":"1984"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-2.1.417"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1137\/0118004"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(88)90040-8"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1968-023-5"},{"key":"e_1_2_1_13_2","volume-title":"Projective Planes","author":"Hughes D. R.","year":"1973"},{"key":"e_1_2_1_14_2","unstructured":"J.Ne\u0161et\u0159ilandV.R\u00f6dl A selective theorem for graphs and hypergraphs in M. Las Vergnas J.\u2010C. Bermond J.\u2010C. Fourier and D. Sotteau (Eds.) Proc. Colloque Inter. CNRS. pp.309\u2013311 1978."},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(88)90076-4"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240030406","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240030406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T15:00:49Z","timestamp":1698073249000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240030406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/rsa.3240030406"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240030406","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}