{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:13:45Z","timestamp":1758824025303},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5697,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove that every connected graph <jats:italic>G<\/jats:italic> contains a tree <jats:italic>T<\/jats:italic> of maximum degree at most <jats:italic>k<\/jats:italic> that either spans <jats:italic>G<\/jats:italic> or has order at least <jats:italic>k<\/jats:italic>\u03b4(<jats:italic>G<\/jats:italic>) + 1, where \u03b4(<jats:italic>G<\/jats:italic>) is the minimum degree of <jats:italic>G.<\/jats:italic> This generalizes and unifies earlier results of Bermond [1] and Win [7]. We also show that the square of a connected graph contains a spanning tree of maximum degree at most three.<\/jats:p>","DOI":"10.1002\/jgt.3190150103","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T06:50:08Z","timestamp":1181285408000},"page":"7-13","source":"Crossref","is-referenced-by-count":8,"title":["On the largest tree of given maximum degree in a connected graph"],"prefix":"10.1002","volume":"15","author":[{"given":"Y.","family":"Caro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Krasikov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"Roditty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"127","volume-title":"Selected Topics in Graph Theory","author":"Bermond J. C.","year":"1978"},{"key":"e_1_2_1_3_2","first-page":"109","article-title":"Spanning trees and some edge\u2010reconstructible graphs","volume":"20","author":"Caro Y.","year":"1985","journal-title":"Ars Combinat."},{"key":"e_1_2_1_4_2","unstructured":"H.Fleischner Hamilton square of graphs.Recent Advances in Graph Theory Proceedings of the Symposium in Prague 1974 (1975)197\u2013206."},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1968-037-0"},{"key":"e_1_2_1_6_2","first-page":"205","volume-title":"Selected Topics in Graph Theory","author":"Nash\u2010Williams C. St. J. A.","year":"1978"},{"key":"e_1_2_1_7_2","unstructured":"V.Neumann\u2010LaraandE.Rivera\u2010Campo Spanning trees with bounded degrees. Submitted."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02995957"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150103","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150103","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T23:04:40Z","timestamp":1698015880000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1991,3]]}},"alternative-id":["10.1002\/jgt.3190150103"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150103","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,3]]}}}