{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T18:20:05Z","timestamp":1719598805827},"reference-count":4,"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":7794,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A graph <jats:italic>G<\/jats:italic> is <jats:italic>uniquely embeddable<\/jats:italic> in a surface <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> if for any two embeddings <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>f<\/jats:italic><jats:sub>2<\/jats:sub>: <jats:italic>G<\/jats:italic> \u2192 <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup>, there exists an isomorphism \u03c3: <jats:italic>G<\/jats:italic> \u2192 <jats:italic>G<\/jats:italic> and a homeomorphism <jats:italic>h<\/jats:italic>: <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> \u2192 <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> for which <jats:italic>h<\/jats:italic> \u2192 <jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub> = <jats:italic>f<\/jats:italic><jats:sub>2<\/jats:sub> \u03c3. A graph <jats:italic>G<\/jats:italic> is <jats:italic>faithfully embeddable<\/jats:italic> in a surface <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> if <jats:italic>G<\/jats:italic> admits an embedding <jats:italic>f: G \u2192 F<\/jats:italic><jats:sup>2<\/jats:sup> such that for any isomorphism \u03c3: <jats:italic>G<\/jats:italic> \u2192 <jats:italic>G<\/jats:italic>, there is a homeomorphism <jats:italic>h<\/jats:italic>: <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> \u2192 <jats:italic>F<\/jats:italic><jats:sup>2<\/jats:sup> with <jats:italic>h<\/jats:italic> \u2192 <jats:italic>f<\/jats:italic> = <jats:italic>f<\/jats:italic> \u2192 \u03c3. It will be shown that if a projective\u2010planar graph <jats:italic>G<\/jats:italic> is 5\u2010connected and contains a subdivision of the complete graph <jats:italic>K<\/jats:italic><jats:sub>6<\/jats:sub> as its subgraph, then <jats:italic>G<\/jats:italic> is uniquely embeddable in a projective plane, and that moreover if <jats:italic>G<\/jats:italic> is not isomorphic to <jats:italic>K<\/jats:italic><jats:sub>6<\/jats:sub>, then <jats:italic>G<\/jats:italic> is faithfully embeddable in a projective plane.<\/jats:p>","DOI":"10.1002\/jgt.3190090206","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:18:19Z","timestamp":1180423099000},"page":"235-243","source":"Crossref","is-referenced-by-count":12,"title":["Unique and faithful embeddings of projective\u2010planar graphs"],"prefix":"10.1002","volume":"9","author":[{"given":"Seiya","family":"Negami","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":"10.1016\/0095-8956(82)90041-7"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90057-2"},{"key":"e_1_2_1_4_2","article-title":"Uniquely and faithfully embeddable projective\u2010planar triangulations","author":"Negami S.","journal-title":"J. Combinatorial Theory, Ser. B."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371086"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090206","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T05:28:42Z","timestamp":1697866122000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,6]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1985,6]]}},"alternative-id":["10.1002\/jgt.3190090206"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090206","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,6]]}}}