{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T18:33:35Z","timestamp":1761762815087},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8982,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a graph with a known triangular embedding in a surface <jats:italic>S<\/jats:italic>, and consider <jats:italic>G<\/jats:italic><jats:sub>(<jats:italic>m<\/jats:italic>)<\/jats:sub>, the composition of <jats:italic>G<\/jats:italic> with an independant set of order <jats:italic>m.<\/jats:italic> The purpose of this paper is to construct a triangular embedding of <jats:italic>G<\/jats:italic><jats:sub>(<jats:italic>m<\/jats:italic>)<\/jats:sub> into a surface <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> by using a covering triangulation with folds. We make the construction for three cases. One of them is used for proving that <jats:italic>G<\/jats:italic><jats:sub>(<jats:italic>m<\/jats:italic>)<\/jats:sub> can be triangularly embedded into a surface <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap> if <jats:italic>G<\/jats:italic> is an Eulerian graph which can be triangularly embedded into a surface <jats:italic>S<\/jats:italic> with the same orientability characteristic as <jats:chem-struct-wrap><jats:chem-struct><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/gif\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/must001.gif\"><jats:alt-text>magnified image<\/jats:alt-text><\/jats:graphic><\/jats:chem-struct><\/jats:chem-struct-wrap>.<\/jats:p>","DOI":"10.1002\/jgt.3190060107","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:33:55Z","timestamp":1180420435000},"page":"57-74","source":"Crossref","is-referenced-by-count":14,"title":["Constructions of covering triangulations with folds"],"prefix":"10.1002","volume":"6","author":[{"given":"Andr\u00e9","family":"Bouchet","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":"10.1007\/BFb0070367"},{"key":"e_1_2_1_3_2","unstructured":"A.Bouchet Covering triangulations with folds.International Conference on the Theory and Applications of Graphs.Kalamazoo MI (1980). 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T.","year":"1973"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:15:06Z","timestamp":1699766106000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["10.1002\/jgt.3190060107"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060107","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,3]]}}}