{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T04:52:24Z","timestamp":1774500744119,"version":"3.50.1"},"reference-count":10,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2005,8,5]],"date-time":"2005-08-05T00:00:00Z","timestamp":1123200000000},"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":[[2006,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>f<\/jats:italic>(<jats:italic>n<\/jats:italic>)\u2009=\u2009min{\u03c7(<jats:italic>G<\/jats:italic>\u2009\u00d7\u2009<jats:italic>H<\/jats:italic>)\u2009:\u2009<jats:italic>G<\/jats:italic> and <jats:italic>H<\/jats:italic> are <jats:italic>n<\/jats:italic>\u2010chromatic digraphs} and <jats:italic>g<\/jats:italic>(<jats:italic>n<\/jats:italic>)\u2009=\u2009min{\u03c7(<jats:italic>G<\/jats:italic>\u2009\u00d7\u2009<jats:italic>H<\/jats:italic>)\u2009:\u2009<jats:italic>G<\/jats:italic> and <jats:italic>H<\/jats:italic> are <jats:italic>n<\/jats:italic>\u2010chromatic graphs}. We prove that <jats:italic>f<\/jats:italic> is bounded if and only if <jats:italic>g<\/jats:italic> is bounded. \u00a9 2005 Wiley Periodicals, Inc. J Graph Theory<\/jats:p>","DOI":"10.1002\/jgt.20117","type":"journal-article","created":{"date-parts":[[2005,8,5]],"date-time":"2005-08-05T16:52:06Z","timestamp":1123260726000},"page":"33-36","source":"Crossref","is-referenced-by-count":8,"title":["Chromatic numbers of products of graphs: The directed and undirected versions of the Poljak\u2010R\u00f6dl function"],"prefix":"10.1002","volume":"51","author":[{"given":"Claude","family":"Tardif","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Wehlau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,8,5]]},"reference":[{"key":"e_1_2_1_2_2","article-title":"The Categorical Product of two 5\u2010chromatic digraphs can be 3\u2010chromatic, preprint 2004, 2 pages MS","author":"Bessy S.","journal-title":"Discrete Math"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579374"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02122553"},{"key":"e_1_2_1_5_2","unstructured":"S. H.Hedetniemi Homomorphisms of graphs and automata University of Michigan Technical Report 03105\u201044\u2010T 1966."},{"key":"e_1_2_1_6_2","first-page":"209","article-title":"Coloring digraphs by iterated antichains","volume":"32","author":"Poljak S.","year":"1991","journal-title":"Comment Math Univ Carolin"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(81)80024-X"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00213-2"},{"key":"e_1_2_1_9_2","volume-title":"Chromatic numbers of products of tournaments: Fractional aspects of Hedetniemi's conjecture, Graphs, Morphisms and Statistical Physics, 171\u2013175 DIMACS Ser Discrete Math Theoret Comput Sci","author":"Tardif C.","year":"2004"},{"key":"e_1_2_1_10_2","unstructured":"C.Tardif The fractional chromatic number of the categorical product of graphs preprint 9 pages MS Combinatorica to appear."},{"key":"e_1_2_1_11_2","first-page":"1","article-title":"A survey on Hedetniemi's conjecture","volume":"2","author":"Zhu X.","year":"1998","journal-title":"Taiwanese J Math"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T22:27:09Z","timestamp":1697668029000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,8,5]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1002\/jgt.20117"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20117","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,8,5]]}}}