{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T08:12:48Z","timestamp":1697703168886},"reference-count":26,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2009,3,13]],"date-time":"2009-03-13T00:00:00Z","timestamp":1236902400000},"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":[[2009,8]]},"abstract":"Abstract<\/jats:title>We study circular choosability, a notion recently introduced by Mohar and Zhu. First, we provide a negative answer to a question of Zhu about circular cliques. We next prove that cch(G<\/jats:italic>)=O<\/jats:italic>(ch(G<\/jats:italic>)+ln|V<\/jats:italic>(G<\/jats:italic>)|) for every graph G<\/jats:italic>. We investigate a generalization of circular choosability, the circular f<\/jats:italic>\u2010choosability, where f<\/jats:italic> is a function of the degrees. We also consider the circular choice number of planar graphs. Mohar asked for the value of \u03c4\u2009\u2254\u2009sup{cch(G<\/jats:italic>)\u2009:\u2009G<\/jats:italic> is planar}, and we prove that 6\u2264\u03c4<\/jats:italic>\u22648, thereby providing a negative answer to another question of Mohar. We also study the circular choice number of planar and outerplanar graphs with prescribed girth, and graphs with bounded density. \u00a9 2009 Wiley Periodicals, Inc. 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