{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:07:52Z","timestamp":1699834072714},"reference-count":8,"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>For every positive integer <jats:italic>c<\/jats:italic>, we construct a pair <jats:italic>G<jats:sub>c<\/jats:sub><\/jats:italic>, <jats:italic>H<jats:sub>c<\/jats:sub><\/jats:italic> of infinite, nonisomorphic graphs both having exactly <jats:italic>c<\/jats:italic> components such that <jats:italic>G<jats:sub>c<\/jats:sub><\/jats:italic> and <jats:italic>H<jats:sub>c<\/jats:sub><\/jats:italic> are hypomorphic, i.e., <jats:italic>G<jats:sub>c<\/jats:sub><\/jats:italic> and <jats:italic>H<jats:sub>c<\/jats:sub><\/jats:italic> have the same families of vertex\u2010deleted subgraphs. This solves a problem of Bondy and Hemminger. Furthermore, the pair <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>H<\/jats:italic><jats:sub>1<\/jats:sub> is an example for a pair of non\u2010isomorphic, hypomorphic, connected graphs also having connected complements\u2014a property not shared by any of the previously known counterexamples to the reconstruction conjecture for infinite graphs.<\/jats:p>","DOI":"10.1002\/jgt.3190060109","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:49:28Z","timestamp":1180421368000},"page":"81-83","source":"Crossref","is-referenced-by-count":2,"title":["Note on the reconstruction of infinite graphs with a fixed finite number of components"],"prefix":"10.1002","volume":"6","author":[{"given":"Thomas","family":"Andreae","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","article-title":"Reconstructing the degree sequence and the number of components of an infinite graph","author":"Andreae T.","journal-title":"Discrete Math."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010306"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(69)80063-3"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(72)90026-3"},{"key":"e_1_2_1_6_2","first-page":"39","article-title":"On the reconstruction of countable forests","volume":"13","author":"Harary F.","year":"1972","journal-title":"Publ. Math. Inst. Beograd"},{"key":"e_1_2_1_7_2","volume-title":"Selected topics in graph theory","author":"Nash\u2010Williams C. St. J. A.","year":"1978"},{"key":"e_1_2_1_8_2","first-page":"503","article-title":"On reconstructing of infinite forests","volume":"13","author":"Ne\u0161et\u0159il J.","year":"1972","journal-title":"Comment. Univ. Math. Carolinae"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90111-X"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060109","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060109","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:14:44Z","timestamp":1699766084000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060109"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["10.1002\/jgt.3190060109"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060109","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]]}}}