{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T07:13:28Z","timestamp":1697699608054},"reference-count":15,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T00:00:00Z","timestamp":1172102400000},"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":[[2007,7]]},"abstract":"Abstract<\/jats:title>Suppose G<\/jats:italic>=(V<\/jats:italic>, E<\/jats:italic>) is a graph and p<\/jats:italic> \u2265 2q<\/jats:italic> are positive integers. A (p<\/jats:italic>, q<\/jats:italic>)\u2010coloring of G<\/jats:italic> is a mapping \u03d5: V<\/jats:italic> \u2192 {0, 1, \u2026, p<\/jats:italic>\u20101} such that for any edge xy<\/jats:italic> of G<\/jats:italic>, q<\/jats:italic> \u2264 |\u03d5(x<\/jats:italic>)\u2010\u03d5(y<\/jats:italic>)| \u2264 p<\/jats:italic>\u2010q<\/jats:italic>. A color\u2010list is a mapping L<\/jats:italic>: V<\/jats:italic> \u2192 $\\cal P$<\/jats:styled-content>({0, 1, \u2026, p<\/jats:italic>\u20101}) which assigns to each vertex v<\/jats:italic> a set L<\/jats:italic>(v<\/jats:italic>) of permissible colors. An L<\/jats:italic>\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010coloring of G<\/jats:italic> is a (p<\/jats:italic>, q<\/jats:italic>)\u2010coloring \u03d5 of G<\/jats:italic> such that for each vertex v<\/jats:italic>, \u03d5(v<\/jats:italic>) \u2208 L<\/jats:italic>(v<\/jats:italic>). We say G<\/jats:italic> is L<\/jats:italic>\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010colorable if there exists an L<\/jats:italic>\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010coloring of G<\/jats:italic>. A color\u2010size\u2010list is a mapping \u2113 which assigns to each vertex v<\/jats:italic> a non\u2010negative integer \u2113(v<\/jats:italic>). We say G<\/jats:italic> is \u2113\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010colorable if for every color\u2010list L<\/jats:italic> with |L<\/jats:italic>(v<\/jats:italic>)| = \u2113(v<\/jats:italic>), G<\/jats:italic> is L<\/jats:italic>\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010colorable. In this article, we consider list circular coloring of trees and cycles. For any tree T<\/jats:italic> and for any p<\/jats:italic> \u2265 2q<\/jats:italic>, we present a necessary and sufficient condition for T<\/jats:italic> to be \u2113\u2010(p<\/jats:italic>, q<\/jats:italic>)\u2010colorable. For each cycle C<\/jats:italic> and for each positive integer k<\/jats:italic>, we present a condition on \u2113 which is sufficient for C<\/jats:italic> to be \u2113\u2010(2k<\/jats:italic>+1, k<\/jats:italic>)\u2010colorable, and the condition is sharp. \u00a9 2007 Wiley Periodicals, Inc. J Graph Theory 55: 249\u2013265, 2007<\/jats:p>","DOI":"10.1002\/jgt.20234","type":"journal-article","created":{"date-parts":[[2007,2,22]],"date-time":"2007-02-22T20:40:04Z","timestamp":1172176804000},"page":"249-265","source":"Crossref","is-referenced-by-count":5,"title":["List circular coloring of trees and cycles"],"prefix":"10.1002","volume":"55","author":[{"given":"Andr\u00e9","family":"Raspaud","sequence":"first","affiliation":[]},{"given":"Xuding","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,2,22]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(03)00081-9"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.2000.2009"},{"key":"e_1_2_1_4_2","unstructured":"M.DeVos Personal Communication at Workshop on Flows and Cycles Simon Fraser University 2000."},{"key":"e_1_2_1_5_2","unstructured":"G.Fijav\u017e M.Juvan B.Mohar andR.\u0160krekovski Circular colorings of planar graphs with prescribed girth manuscript (2001)."},{"key":"e_1_2_1_6_2","first-page":"391","article-title":"On circular flows in graphs, Finite and Infinite Sets (Eger, 1981)","volume":"37","author":"Jaeger F.","year":"1984","journal-title":"Colloquia Mathematica Societatis J\u00e1nos Bolyai"},{"key":"e_1_2_1_7_2","first-page":"71","volume-title":"Selected Topics in Graph Theory 3","author":"Jaeger F.","year":"1988"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(200002)33:2<109::AID-JGT5>3.0.CO;2-F"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.10171"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1994.1062"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1995.1027"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120411"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","first-page":"#R25","DOI":"10.37236\/1569","article-title":"The circular chromatic number of planar graphs of large odd girth","author":"Zhu X.","year":"2001","journal-title":"Electronic J Combin"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(00)00217-X"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-33700-8_25"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20051"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.20234","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.20234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T19:15:45Z","timestamp":1697656545000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.20234"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,2,22]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,7]]}},"alternative-id":["10.1002\/jgt.20234"],"URL":"https:\/\/doi.org\/10.1002\/jgt.20234","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,2,22]]}}}