{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T17:41:07Z","timestamp":1697910067122},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8342,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1983,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A product dimension of bipartite graphs bid <jats:italic>G<\/jats:italic> analogous to the Dushnik\u2010Miller dimension of posets and to the dimension of general symmetric graphs is studied. It is shown that bid<jats:italic>G \u2266 1\/2|V(G)|<\/jats:italic> + 1 and almost all bipartite graphs <jats:italic>G<\/jats:italic> have bid<jats:italic>G<\/jats:italic> close to 1\/2|V(G)|. On the other hand it is shown to be considerably less for everyday graphs like trees, cycles, cubes, etc.<\/jats:p>","DOI":"10.1002\/jgt.3190070414","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:07:53Z","timestamp":1180422473000},"page":"475-486","source":"Crossref","is-referenced-by-count":5,"title":["On a product dimension of bipartite graphs"],"prefix":"10.1002","volume":"7","author":[{"given":"S.","family":"Poljak","sequence":"first","affiliation":[]},{"given":"D.","family":"R\u00f6dl","sequence":"additional","affiliation":[]},{"given":"A.","family":"Pultr","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2371374"},{"key":"e_1_2_1_3_2","volume-title":"Probabilistic Methods in Combinatorics","author":"Erd\u00f6s P.","year":"1974"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(80)90043-X"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90186-3"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"O.Ore Theory of Graphs AMS Colloq. Publ. Vol. 38 Providence (1962).","DOI":"10.1090\/coll\/038"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(81)90064-9"},{"key":"e_1_2_1_8_2","volume-title":"18. Combinatorics","author":"Pultr A.","year":"1978"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90055-3"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01171114"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(75)90031-X"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190070414","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190070414","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T09:22:27Z","timestamp":1697793747000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190070414"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1983,12]]}},"alternative-id":["10.1002\/jgt.3190070414"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190070414","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,12]]}}}