{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:21:54Z","timestamp":1759335714652,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>It was conjectured by Jaeger that $4k$-edge connected graphs admit a $(2k+1, k)$-flow. The restriction of this conjecture to planar graphs is equivalent to the statement that planar graphs of girth at least $4k$ have circular chromatic number at most $2+ {{1}\\over {k}}$. Even this restricted version of Jaeger's conjecture is largely open. The $k=1$ case is the well-known Gr\u00f6tzsch 3-colour theorem. This paper proves that for $k \\geq 2$, planar graphs of odd girth at least $8k-3$ have circular chromatic number at most $2+{{1}\\over {k}}$.<\/jats:p>","DOI":"10.37236\/1569","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:07:24Z","timestamp":1578690444000},"source":"Crossref","is-referenced-by-count":17,"title":["Circular Chromatic Number of Planar Graphs of Large Odd Girth"],"prefix":"10.37236","volume":"8","author":[{"given":"Xuding","family":"Zhu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,6,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r25\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1r25\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:17:51Z","timestamp":1579306671000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1r25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,6,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1569","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,6,7]]},"article-number":"R25"}}