{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T07:13:25Z","timestamp":1726384405624},"reference-count":5,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":6182,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1989,11]]},"abstract":"Abstract<\/jats:title>Let G<\/jats:italic> = (V,E<\/jats:italic>) be an undirected graph. A subset F<\/jats:italic> of E<\/jats:italic> is a matching cutset of G<\/jats:italic> if no two edges of F<\/jats:italic> are incident with the same point, and G\u2010F<\/jats:italic> has more components than G<\/jats:italic>. Chv\u0301atal [2] proved that it is NP\u2010complete to recognize graphs with a matching cutset even if the input is restricted to graphs with maximum degree 4. We prove the following: (a) Every connected graph with maximum degree \u2a7d3 and on more than 7 points has a matching cutset. (In particular, there are precisely two connected cubic graphs without a matching cutset). (b) Line graphs with a matching cutset can be recognized in O<\/jats:italic>(|E<\/jats:italic>|) time. (c) Graphs without a chordless circuit of length 5 or more that have a matching cutset can be recognized in O<\/jats:italic>(|V<\/jats:italic>||E<\/jats:italic>|3<\/jats:sup>) time.<\/jats:p>","DOI":"10.1002\/jgt.3190130502","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T13:53:23Z","timestamp":1181310803000},"page":"527-536","source":"Crossref","is-referenced-by-count":35,"title":["Matching cutsets in graphs"],"prefix":"10.1002","volume":"13","author":[{"given":"Augustine M.","family":"Moshi","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graphs","author":"Berge C.","year":"1985"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190080106"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1970.tb56468.x"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/321850.321853"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01904834"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190130502","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190130502","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T02:21:04Z","timestamp":1697941264000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190130502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,11]]},"references-count":5,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1989,11]]}},"alternative-id":["10.1002\/jgt.3190130502"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190130502","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,11]]}}}