{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:20:34Z","timestamp":1758824434689,"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>A pair $(G,\\sigma)$ is called a {\\it signed graph} if $\\sigma: E(G) \\longrightarrow \\{1,-1\\}$ is a mapping which assigns to each edge $e$ of $G$ a sign $\\sigma(e) \\in \\{1,-1\\}$. If $(G,\\sigma)$ is a signed graph, then a {\\it complex-4-coloring} of $(G,\\sigma)$ is a mapping $f: V(G) \\longrightarrow \\{1,-1,i,-i\\}$ with $i=\\sqrt{-1}$ such that $f(u)f(v) \\not= \\sigma(e)$ for every edge $e=uv$ of $G$.\r\nWe prove that there are signed planar graphs that are not complex-$4$-colorable. This result completes investigations of Jin, Wong and Zhu as well as Jiang and Zhu on $4$-colorings of generalized signed planar graphs disproving a conjecture of the latter authors.<\/jats:p>","DOI":"10.37236\/9844","type":"journal-article","created":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T10:25:26Z","timestamp":1620296726000},"source":"Crossref","is-referenced-by-count":2,"title":["A Note on Complex-4-Colorability of Signed Planar Graphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Arnfried","family":"Kemnitz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Margit","family":"Voigt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,5,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i2p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T10:25:26Z","timestamp":1620296726000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i2p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,7]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,4,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9844","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,5,7]]},"article-number":"P2.17"}}