{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T13:11:25Z","timestamp":1698412285498},"reference-count":20,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The problem of when a recursive graph has a recursive <jats:italic>k<\/jats:italic>\u2010coloring has been extensively studied by Bean, Schmerl, Kierstead, Remmel, and others. In this paper, we study the polynomial time analogue of that problem. We develop a number of negative and positive results about colorings of polynomial time graphs. For example, we show that for any recursive graph <jats:italic>G<\/jats:italic> and for any <jats:italic>k<\/jats:italic>, there is a polynomial time graph <jats:italic>G<\/jats:italic>\u2032 whose vertex set is {0,1}* such that there is an effective degree preserving correspondence between the set of <jats:italic>k<\/jats:italic>\u2010colorings of <jats:italic>G<\/jats:italic> and the set of <jats:italic>k<\/jats:italic>\u2010colorings of <jats:italic>G<\/jats:italic>\u2032 and hence there are many examples of <jats:italic>k<\/jats:italic>\u2010colorable polynomial time graphs with no recursive <jats:italic>k<\/jats:italic>\u2010colorings. Moreover, even though every connected 2\u2010colorable recursive graph is recursively 2\u2010colorable, there are connected 2\u2010colorable polynomial time graphs which have no primitive recursive 2\u2010coloring. We also give some sufficient conditions which will guarantee that a polynomial time graph has a polynomial time or exponential time coloring.<\/jats:p>","DOI":"10.1002\/malq.19950410305","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:46:51Z","timestamp":1180201611000},"page":"327-352","source":"Crossref","is-referenced-by-count":9,"title":["Feasible Graphs and Colorings"],"prefix":"10.1002","volume":"41","author":[{"given":"Douglas","family":"Cenzer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeffrey","family":"Remmel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","first-page":"429","article-title":"Every planar map is 4\u2010colorable","volume":"21","author":"Appel K.","year":"1977","journal-title":"Ill. J. 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T.Trotter On\u2010line and first\u2010fite coloring of graphs which do not induceP5.To appear."},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90051-5"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-3466-1_18"},{"key":"e_1_2_1_19_2","volume-title":"Theory of Recursive Functions and Effective Computability","author":"Rogers H.","year":"1967"},{"key":"e_1_2_1_20_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1980-062-7"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1982-075-6"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410305","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:45:55Z","timestamp":1698331555000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410305"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410305","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}