{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:55Z","timestamp":1759063555594},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2008,2,24]],"date-time":"2008-02-24T00:00:00Z","timestamp":1203811200000},"content-version":"vor","delay-in-days":5654,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1992,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A <jats:italic>k<\/jats:italic>\u2010graph, <jats:italic>H<\/jats:italic> = (<jats:italic>V, E<\/jats:italic>), is <jats:italic>tight<\/jats:italic> if for every surjective mapping <jats:italic>f<\/jats:italic>: <jats:italic>V<\/jats:italic> \u2192 {1,\u2026.k} there exists an edge \u03b1 \u03f5 <jats:italic>E<\/jats:italic> sicj tjat <jats:italic>f<\/jats:italic>|<jats:sub>\u03b1<\/jats:sub> is injective. Clearly, 2\u2010graphs are tight if and only if they are connected. Bounds for the minimum number \u03d5<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-1.gif\" xlink:title=\"urn:x-wiley:03649024:media:JGT3190160405:tex2gif-stack-1\" \/> of edges in a tight <jats:italic>k<\/jats:italic>\u2010graph with <jats:italic>n<\/jats:italic> vertices are given. We conjecture that \u03d5<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-stack-2.gif\" xlink:title=\"urn:x-wiley:03649024:media:JGT3190160405:tex2gif-stack-2\" \/> for every <jats:italic>n<\/jats:italic> and prove the equality when 2<jats:italic>n<\/jats:italic> + 1 is prime. From the examples, minimal embeddings of complete graphs into surfaces follow. \u00a9 1992 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/jgt.3190160405","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:53:50Z","timestamp":1181285630000},"page":"319-326","source":"Crossref","is-referenced-by-count":25,"title":["On the minimum size of tight hypergraphs"],"prefix":"10.1002","volume":"16","author":[{"given":"Jorge L.","family":"Arocha","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier","family":"Bracho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Neumann\u2010Lara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2008,2,24]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J. L.Arocha J.Bracho andV.Neumann\u2010Lara On tightkgraphs. In preparation."},{"key":"e_1_2_1_3_2","unstructured":"J. L.Arocha J.Bracho andV.Neumann\u2010Lara Tight and untight triangulated surfaces. Preprint."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","DOI":"10.1090\/cbms\/045","volume-title":"Rudiments of Ramsey Theory","author":"Graham R. L.","year":"1981"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01637280"},{"key":"e_1_2_1_6_2","first-page":"1","volume-title":"Graph theory and related topics","author":"Lov\u00e1sz L.","year":"1979"},{"key":"e_1_2_1_7_2","unstructured":"V.Neumann\u2010Lara The acyclic disconnection of a digraph. In preparation."},{"key":"e_1_2_1_8_2","volume-title":"Map Color Theorem. Die Grundlehren der Mathematischen Wissenchaften, Band 209","author":"Ringel G.","year":"1974"},{"key":"e_1_2_1_9_2","first-page":"114","article-title":"Uber die Kongruenz x\n                  m + y\n                  m \uf8fd z\n                  m(mod p)","volume":"25","author":"Schur I.","year":"1916","journal-title":"Jber. Deutsche Math. Verein."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190160405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190160405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T19:07:47Z","timestamp":1698088067000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190160405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1992,9]]}},"alternative-id":["10.1002\/jgt.3190160405"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190160405","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,9]]}}}