{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T05:36:01Z","timestamp":1771911361223,"version":"3.50.1"},"reference-count":13,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T00:00:00Z","timestamp":1159920000000},"content-version":"vor","delay-in-days":6882,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1987,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a graph, and let <jats:italic>D<\/jats:italic> be a directed graph. Write <jats:italic>G \u2192 D<\/jats:italic> to mean that, no matter how the edges of <jats:italic>G<\/jats:italic> are given orientations, a copy of <jats:italic>D<\/jats:italic> must appear as a subgraph of the resulting oriented graph. It is proved that among all <jats:italic>G<\/jats:italic> for which <jats:italic>G \u2192 D<\/jats:italic>, the minimum chromatic number is equal to the minimum <jats:italic>k<\/jats:italic> for which <jats:italic>K<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub> \u2192 hom(<jats:italic>D<\/jats:italic>), where hom(<jats:italic>D<\/jats:italic>) is the set of homomorphs of <jats:italic>D<\/jats:italic>. Next, necessary and sufficient conditions are given for a directed graph to have a homomorphism into a given transitive tournament, directed path, or directed cycle. These results are then applied to various cases of the above theorem. In particular, the minimum chromatic number is evaluated whenever <jats:italic>D<\/jats:italic> is an oriented forest, and all <jats:italic>D<\/jats:italic> are characterized for which the minimum chromatic number is no more than three.<\/jats:p>","DOI":"10.1002\/jgt.3190110402","type":"journal-article","created":{"date-parts":[[2007,6,9]],"date-time":"2007-06-09T02:53:32Z","timestamp":1181357612000},"page":"453-462","source":"Crossref","is-referenced-by-count":12,"title":["On unavoidable digraphs in orientations of graphs"],"prefix":"10.1002","volume":"11","author":[{"given":"Gary S.","family":"Bloom","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan A.","family":"Burr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,4]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"58","volume-title":"Topics in Graph Theory","author":"Burr S. A.","year":"1979"},{"key":"e_1_2_1_3_2","first-page":"227","article-title":"Subtrees of directed graphs and hypergraphs","volume":"28","author":"Burr S. A.","year":"1980","journal-title":"Congressus Numerantium"},{"key":"e_1_2_1_4_2","first-page":"167","article-title":"On graphs of Ramsey type","volume":"1","author":"Burr S. A.","year":"1976","journal-title":"Ars Combinat."},{"key":"e_1_2_1_5_2","unstructured":"R.H\u00e4ggkvist P.Hell D. J.Miller andV.Neumann\u2010Lara On Multiplicative graphs and the product conjecture. Report University of Stockholm (1985); to appear inCombinatorica."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/2315334"},{"key":"e_1_2_1_8_2","volume-title":"The Art of Computer Programming, vol. 1, Fundamental Algorithms","author":"Knuth D. E.","year":"1973"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"50","DOI":"10.4064\/cm-3-1-50-57","article-title":"On a problem of K. Zarankiewicz","volume":"3","author":"K\u00f6v\u00e1ri T.","year":"1969","journal-title":"Colloq. Math."},{"key":"e_1_2_1_10_2","volume-title":"Topics on Tournaments","author":"Moon J. W.","year":"1968"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90062-6"},{"key":"e_1_2_1_12_2","first-page":"39","article-title":"Ein kombinatorischer Satz","volume":"7","author":"R\u00e9dei L.","year":"1934","journal-title":"Acta Litt. Szeged"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(74)90069-0"},{"key":"e_1_2_1_14_2","first-page":"127","article-title":"Nombre chromatique et plus longs chemins d'un graphe","volume":"1","author":"Roy B.","year":"1967","journal-title":"Revue AFIRO"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190110402","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190110402","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T09:35:02Z","timestamp":1697880902000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190110402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987,12]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1987,12]]}},"alternative-id":["10.1002\/jgt.3190110402"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190110402","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1987,12]]}}}