{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T05:40:39Z","timestamp":1697866839657},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":8350,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Networks"],"published-print":{"date-parts":[[1983,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The matching polyhedron theorem of Edmonds and Johnson, which gives the convex hull of capacitated perfect <jats:italic>b<\/jats:italic>\u2010matchings of a bidirected graph, is proved by reducing this matching problem to the ordinary perfect 1\u2013matching problem, for which there exists a short inductive proof of the corresponding polyhedral theorem. The proof method makes it possible to deduce nestedness and discreteness properties of optimal dual solutions to the general matching problem from analogous properties of optimal dual solutions to the perfect 1\u2013matching problem. In particular, the total dual half\u2010integrality of the inequality system for general matching is shown to follow from that for 1\u2013matching. Applications considered include determining the convex hull of unions of disjoint circuits of a graph.<\/jats:p>","DOI":"10.1002\/net.3230130403","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T17:19:01Z","timestamp":1178903941000},"page":"455-473","source":"Crossref","is-referenced-by-count":15,"title":["Reductions to 1\u2013matching polyhedra"],"prefix":"10.1002","volume":"13","author":[{"given":"Julian","family":"Ar\u00e1oz","sequence":"first","affiliation":[]},{"given":"William H.","family":"Cunningham","sequence":"additional","affiliation":[]},{"given":"Jack","family":"Edmonds","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Green\u2010Kr\u00f3tki","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1965-045-4"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.013"},{"key":"e_1_2_1_4_2","first-page":"89","volume-title":"Combinatorial Structures and their Applications","author":"Edmonds J.","year":"1970"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580113"},{"key":"e_1_2_1_6_2","unstructured":"J.Green\u2010Kr\u00f3tki Matching polyhedra. M.Sc. Thesis Carleton University 1980."},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","unstructured":"W. R.Pulleyblank Faces of matching polyhedra. Ph.D. Thesis University of Waterloo 1973.","DOI":"10.1007\/BFb0066196"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(83)90011-4"},{"key":"e_1_2_1_9_2","first-page":"341","volume-title":"Graph Theory and Related Topics","author":"Seymour P. D.","year":"1979"}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230130403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230130403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T02:59:11Z","timestamp":1697770751000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230130403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,12]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1983,12]]}},"alternative-id":["10.1002\/net.3230130403"],"URL":"https:\/\/doi.org\/10.1002\/net.3230130403","archive":["Portico"],"relation":{},"ISSN":["0028-3045","1097-0037"],"issn-type":[{"value":"0028-3045","type":"print"},{"value":"1097-0037","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,12]]}}}