{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T03:08:02Z","timestamp":1768532882896,"version":"3.49.0"},"reference-count":14,"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 following type of problem arises in practice: in a node\u2010weighted graph <jats:italic>G<\/jats:italic>, find a minimum\u2010weight node set that satisfies certain conditions and, in addition, induces a perfectly matchable subgraph of <jats:italic>G.<\/jats:italic> This has led us to study the convex hull of incidence vectors of node sets that induce perfectly matchable subgraphs of a graph <jats:italic>G<\/jats:italic>, which we call the perfectly matchable subgraph polytope of <jats:italic>G.<\/jats:italic> For the case when <jats:italic>G<\/jats:italic> is bipartite, we give a linear characterization of this polytope, i.e., specify a system of linear inequalities whose basic solutions are the incidence vectors of perfectly matchable node sets of <jats:italic>G.<\/jats:italic> We derive this result by three different approaches, using linear programming duality, projection, and lattice polyhedra, respectively. The projection approach is used here for the first time as a proof method in polyhedral combinatorics, and seems to have many similar applications. Finally, we completely characterize the facets of our polytope; i.e., we separate the essential inequalities of our linear defining system from the redundant ones.<\/jats:p>","DOI":"10.1002\/net.3230130405","type":"journal-article","created":{"date-parts":[[2007,5,11]],"date-time":"2007-05-11T17:18:38Z","timestamp":1178903918000},"page":"495-516","source":"Crossref","is-referenced-by-count":82,"title":["The perfectly matchable subgraph polytope of a bipartite graph"],"prefix":"10.1002","volume":"13","author":[{"given":"Egon","family":"Balas","sequence":"first","affiliation":[]},{"given":"William","family":"Pulleyblank","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":"10.1007\/BF01386316"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01584082"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70817-3"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.016"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70734-9"},{"key":"e_1_2_1_7_2","first-page":"239","article-title":"Lattice polyhedra II: Generalizations, constructions and examples","volume":"15","author":"Gr\u00f6flin H.","year":"1982","journal-title":"Ann. Discrete Math."},{"key":"e_1_2_1_8_2","volume-title":"Polyedrische Charakterisierungen kombinatorischer Optimierungs\u2010probleme","author":"Gr\u00f6tschel M.","year":"1977"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-10.37.26"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0121202"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01580250"},{"key":"e_1_2_1_12_2","first-page":"593","volume-title":"Combinatorics (Proceedings of the 5th Hungarian Colloquium on Combinatorics","author":"Hoffman A. J.","year":"1976"},{"key":"e_1_2_1_13_2","volume-title":"Theorie der endlichen und unendlichen Graphen","author":"K\u00f6nig D.","year":"1936"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(81)90005-7"},{"key":"e_1_2_1_15_2","unstructured":"A.Schrijver private communication."}],"container-title":["Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnet.3230130405","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/net.3230130405","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T02:59:21Z","timestamp":1697770761000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/net.3230130405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1983,12]]}},"alternative-id":["10.1002\/net.3230130405"],"URL":"https:\/\/doi.org\/10.1002\/net.3230130405","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]]}}}