{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T08:12:55Z","timestamp":1697703175860},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2009,3,23]],"date-time":"2009-03-23T00:00:00Z","timestamp":1237766400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2009,5]]},"abstract":"Abstract<\/jats:title>In this paper we introduce the concept of fair reception of a graph which is related to its domination number. We prove that all graphs G<\/jats:italic> with a fair reception of size \u03b3(G<\/jats:italic>) satisfy Vizing's conjecture on the domination number of Cartesian product graphs, by which we extend the well\u2010known result of Barcalkin and German concerning decomposable graphs. Combining our concept with a result of Aharoni, Berger and Ziv, we obtain an alternative proof of the theorem of Aharoni and Szab\u00f3 that chordal graphs satisfy Vizing's conjecture. A new infinite family of graphs that satisfy Vizing's conjecture is also presented. \u00a9 2009 Wiley Periodicals, Inc. J Graph Theory 61: 45\u201054, 2009<\/jats:p>","DOI":"10.1002\/jgt.20366","type":"journal-article","created":{"date-parts":[[2009,3,23]],"date-time":"2009-03-23T18:17:06Z","timestamp":1237832226000},"page":"45-54","source":"Crossref","is-referenced-by-count":18,"title":["Fair reception and Vizing's conjecture"],"prefix":"10.1002","volume":"61","author":[{"given":"Bo\u0161tjan","family":"Bre\u0161ar","sequence":"first","affiliation":[]},{"given":"Douglas F.","family":"Rall","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,3,23]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s004930200016"},{"key":"e_1_2_1_3_2","unstructured":"R.AharoniandT.Szab\u00f3 Vizing's Conjecture for chordal graphs manuscript (http:\/\/www.inf.ethz.ch\/personal\/szabo\/honpub.html)."},{"key":"e_1_2_1_4_2","first-page":"5","article-title":"The external stability number of the Cartesian product of graphs","volume":"1","author":"Barcalkin A. M.","year":"1979","journal-title":"Bul Acad Stiinte RSS Moldovenesti"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1129"},{"issue":"1","key":"e_1_2_1_6_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.37236\/1542","article-title":"An inequality related to Vizing's conjecture","volume":"7","author":"Clark W. E.","year":"2000","journal-title":"Electron J Combin"},{"key":"e_1_2_1_7_2","unstructured":"W.Goddard personal communication."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1018"},{"key":"e_1_2_1_9_2","first-page":"163","volume-title":"Domination in Graphs: Advanced Topics","author":"Hartnell B.","year":"1998"},{"key":"e_1_2_1_10_2","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"e_1_2_1_11_2","volume-title":"Product graphs: Structure and Recognition","author":"Imrich W.","year":"2000"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.09.003"},{"key":"e_1_2_1_13_2","first-page":"30","article-title":"Cartesian product of graphs","volume":"9","author":"Vizing V. G.","year":"1963","journal-title":"Vychisl Sistemy"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20366","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20366","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T22:51:33Z","timestamp":1697669493000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20366"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,23]]},"references-count":12,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,5]]}},"alternative-id":["10.1002\/jgt.20366"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20366","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,23]]}}}