{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:26Z","timestamp":1753893806879,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For a real number $r\\ge 2$, a circular $r$-colouring of a signed graph $(G, \\sigma)$ is a mapping $c: V(G)\\to [0, r)$ such that $|c(x)-c(y)|\\in [1,r-1]$ for each positive edge $xy$ and $|c(x)-c(y)|\\in [0,r\/2-1]\\cup [r\/2+1,r)$ for each negative edge $xy$. This concept is recently introduced by Naserasr, Wang, and Zhu in 2021, and they show that for any $\\varepsilon&gt;0$, there exist signed planar bipartite graphs (of girth 4) which are not circular $(4-\\varepsilon)$-colourable. In this paper, we prove that for each signed planar graph $(G, \\sigma)$ of girth at least $5$, there exists a real number $\\varepsilon=\\varepsilon(G,\\sigma)&gt;0$ such that $(G, \\sigma)$ is circular $(4-\\varepsilon)$-colorable. Our proof utilizes a Thomassen-type inductive argument on the dual version in terms of circular flows, which is motivated by a result of Richter, Thomassen, and Younger (2016) on group connectivity of $5$-edge-connected planar graphs.<\/jats:p>","DOI":"10.37236\/12168","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T14:03:10Z","timestamp":1744380190000},"source":"Crossref","is-referenced-by-count":0,"title":["Every Signed Planar Graph of Girth 5 Has Circular Chromatic Number Strictly Less Than 4"],"prefix":"10.37236","volume":"32","author":[{"given":"Jiaao","family":"Li","sequence":"first","affiliation":[]},{"given":"Xueliang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Zhiqian","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2025,4,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T14:03:10Z","timestamp":1744380190000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,11]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/12168","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,4,11]]},"article-number":"P2.2"}}