{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T17:10:54Z","timestamp":1698253854840},"reference-count":12,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,6]],"date-time":"2006-10-06T00:00:00Z","timestamp":1160092800000},"content-version":"vor","delay-in-days":4480,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1994,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, we show that if a 3\u2010connected graph <jats:italic>G<\/jats:italic> other than <jats:italic>K<\/jats:italic><jats:sub>4<\/jats:sub> has a vertex subset <jats:italic>K<\/jats:italic> that covers the set of contractible edges of <jats:italic>G<\/jats:italic> and if |<jats:italic>K<\/jats:italic>| 3 and |<jats:italic>V(G)<\/jats:italic>| 3|<jats:italic>K<\/jats:italic>| \u2212 1, then <jats:italic>K<\/jats:italic> is a cutset of <jats:italic>G<\/jats:italic>. We also give examples to show that this result is best possible. In particular, the result does not hold for <jats:italic>K<\/jats:italic> with smaller cardinality.<\/jats:p>","DOI":"10.1002\/jgt.3190180410","type":"journal-article","created":{"date-parts":[[2007,6,7]],"date-time":"2007-06-07T18:18:35Z","timestamp":1181240315000},"page":"401-411","source":"Crossref","is-referenced-by-count":1,"title":["3\u2010connected graphs with non\u2010cut contractible edge covers of size <i>k<\/i>"],"prefix":"10.1002","volume":"18","author":[{"given":"Xingxing","family":"Yu","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,6]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(87)90065-7"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(92)90040-5"},{"key":"e_1_2_1_4_2","volume-title":"Graph Theory with Applications","author":"Bondy J. A.","year":"1981"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130105"},{"key":"e_1_2_1_6_2","first-page":"291","article-title":"On contractible edges in 3\u2010connected graphs","volume":"38","author":"Dean N.","year":"1987","journal-title":"Congres. Numer."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02992931"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190170212"},{"key":"e_1_2_1_9_2","volume-title":"Combinatorial Problems and Exercises","author":"Lov\u00e1sz L.","year":"1979"},{"key":"e_1_2_1_10_2","first-page":"101","article-title":"Non\u2010separating induced cycles in 3\u2010connected graphs","volume":"2","author":"Ota K.","year":"1988","journal-title":"Scientia Ser. A"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190140603"},{"key":"e_1_2_1_12_2","unstructured":"A.Saito Personal communication with R. L. Hemminger (1988)."},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(61)50045-5"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190180410","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190180410","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,24]],"date-time":"2023-10-24T16:21:51Z","timestamp":1698164511000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190180410"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,7]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1994,7]]}},"alternative-id":["10.1002\/jgt.3190180410"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190180410","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,7]]}}}