{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,3]],"date-time":"2023-11-03T00:54:20Z","timestamp":1698972860330},"reference-count":11,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2009,5,11]],"date-time":"2009-05-11T00:00:00Z","timestamp":1242000000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2010,3]]},"abstract":"Abstract<\/jats:title>Let \ud835\udcaf be the class of unlabeled trees. An unlabeled vertex\u2010deleted subgraph of a tree T<\/jats:italic> is called a card. A collection of cards is called a deck. We say that the tree T<\/jats:italic> has a deck D<\/jats:italic> if each card in D<\/jats:italic> can be obtained by deleting distinct vertices of T<\/jats:italic>. If T<\/jats:italic> is the only unlabeled tree that has the deck D<\/jats:italic>, we say that T<\/jats:italic> is \ud835\udcaf\u2010reconstructible from D<\/jats:italic>. We want to know how large of a deck D<\/jats:italic> is necessary for T<\/jats:italic> to be \ud835\udcaf\u2010reconstructible. We define \ud835\udcafrn(T<\/jats:italic>) as the minimum number of cards in a deck D<\/jats:italic> such that T<\/jats:italic> is \ud835\udcaf\u2010reconstructible from D<\/jats:italic>. It is known that \n\ud835\udcafrn(T<\/jats:italic>)\u22643, but it is conjectured that \ud835\udcafrn(T<\/jats:italic>)\u22642 for all trees T<\/jats:italic>. We prove that the conjecture holds for all homeomorphically irreducible trees. \u00a9 2009 Wiley Periodicals, Inc. J Graph Theory 63: 243\u2013257, 2010<\/jats:p>","DOI":"10.1002\/jgt.20424","type":"journal-article","created":{"date-parts":[[2009,5,11]],"date-time":"2009-05-11T18:29:22Z","timestamp":1242066562000},"page":"243-257","source":"Crossref","is-referenced-by-count":0,"title":["Reconstructing trees from two cards"],"prefix":"10.1002","volume":"63","author":[{"given":"Manuel","family":"Welhan","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,5,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100044364"},{"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":"10.1093\/qmath\/39.1.47"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1966-079-8"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1957.7.961"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90023-7"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90044-8"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01788141"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1970-007-4"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140203"},{"key":"e_1_2_1_12_2","unstructured":"G.Prins The automorphism group of a tree Doctoral dissertation University of Michigan 1957."}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20424","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20424","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T06:21:00Z","timestamp":1698906060000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20424"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,11]]},"references-count":11,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1002\/jgt.20424"],"URL":"http:\/\/dx.doi.org\/10.1002\/jgt.20424","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5,11]]}}}
