{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:12:21Z","timestamp":1699834341624},"reference-count":14,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8890,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The toroidal thickness <jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic>) of a graph <jats:italic>G<\/jats:italic> is the minimum value of <jats:italic>k<\/jats:italic> such that <jats:italic>G<\/jats:italic> is the union of <jats:italic>k<\/jats:italic> graphs each of which is embeddable on a torus. We find <jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic><jats:sub><jats:italic>m<\/jats:italic><\/jats:sub>), where <jats:italic>G<jats:sub>m<\/jats:sub><\/jats:italic> is the graph obtained from the complete graph <jats:italic>K<jats:sub>m<\/jats:sub><\/jats:italic> by removing a Hamiltonian cycle, and we show that <jats:italic>t<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>K<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic>(3)<\/jats:sub>) = [1\/2<jats:italic>n<\/jats:italic>] for many values of <jats:italic>n.<\/jats:italic> The method of approach involves the construction of sets of triples related to Skolem triples.<\/jats:p>","DOI":"10.1002\/jgt.3190060212","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:55:39Z","timestamp":1180421739000},"page":"177-184","source":"Crossref","is-referenced-by-count":6,"title":["On the toroidal thickness of graphs"],"prefix":"10.1002","volume":"6","author":[{"given":"Ian","family":"Anderson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190020306"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1969-109-4"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70182-1"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1017\/S0025557200041693","article-title":"On Langford's problem","volume":"43","author":"Davies R. O.","year":"1959","journal-title":"Math. Gaz."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1960.tb03950.x"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"154","DOI":"10.7146\/math.scand.a-10603","article-title":"A note on Steiner triple systems","volume":"8","author":"Hanani H.","year":"1960","journal-title":"Math. Scand."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01445363"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"208","DOI":"10.7146\/math.scand.a-10931","article-title":"On Steiner and similar triple systems","volume":"24","author":"Hilton A. J. W.","year":"1969","journal-title":"Math. 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Cas."},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-10490"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(78)90036-9"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060212","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060212","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:21:48Z","timestamp":1699766508000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060212"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["10.1002\/jgt.3190060212"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060212","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}