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Algorithms"],"published-print":{"date-parts":[[2010,11]]},"abstract":"<jats:p>\n            In this article we present algorithms for computing large matchings in 3-regular graphs, graphs with maximum degree 3, and 3-connected planar graphs. The algorithms give a guarantee on the size of the computed matching and take linear or slightly superlinear time. Thus they are faster than the best-known algorithm for computing maximum matchings in general graphs, which runs in\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>nm<\/jats:italic>\n            ) time, where\n            <jats:italic>n<\/jats:italic>\n            denotes the number of vertices and\n            <jats:italic>m<\/jats:italic>\n            the number of edges of the given graph. For the classes of 3-regular graphs and graphs with maximum degree 3, the bounds we achieve are known to be best possible.\n          <\/jats:p>\n          <jats:p>\n            We also investigate graphs with block trees of bounded degree, where the\n            <jats:italic>d<\/jats:italic>\n            -block tree is the adjacency graph of the\n            <jats:italic>d<\/jats:italic>\n            -connected components of the given graph. In 3-regular graphs and 3-connected planar graphs with bounded-degree 2- and 4-block trees, respectively, we show how to compute\n            <jats:italic>maximum<\/jats:italic>\n            matchings in slightly superlinear time.\n          <\/jats:p>","DOI":"10.1145\/1868237.1868238","type":"journal-article","created":{"date-parts":[[2010,12,14]],"date-time":"2010-12-14T16:00:46Z","timestamp":1292342446000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Computing large matchings fast"],"prefix":"10.1145","volume":"7","author":[{"given":"Ignaz","family":"Rutter","sequence":"first","affiliation":[{"name":"Universit\u00e4t Karlsruhe (TH), KIT, Karlsruhe, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Wolff","sequence":"additional","affiliation":[{"name":"Technische Universiteit Eindhoven, W\u00fcrzburg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2010,12,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1098-2418(199803)12:2%3C111::AID-RSA1%3E3.0.CO;2-#"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'01)","author":"Biedl T.","year":"2001"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2000.1132"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.05.003"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(89)90012-6"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s004930170002"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/28395.28396"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2005.05.007"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/321941.321942"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2001.1167"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90294-4"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/502090.502095"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1991.185451"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195997000132"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(94)00304-2"},{"key":"e_1_2_1_17_1","unstructured":"Lov\u00e1sz L. and Plummer M. D. 1986. Matching Theory. North Holland Amsterdam The Netherlands.  Lov\u00e1sz L. and Plummer M. D. 1986. Matching Theory. North Holland Amsterdam The Netherlands."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1980.12"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539789162997"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.40"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-005-1187-5"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90133-X"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392606"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(97)00019-9"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539796299266"},{"key":"e_1_2_1_26_1","unstructured":"Strothmann W.-B. 1997. Bounded degree spanning trees. Ph.D. dissertation. 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