{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:47:58Z","timestamp":1761709678565,"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>Let $G$ be a plane graph whose vertices are to be colored subject to constraints on some of the faces. There are 3 types of constraints: a $C$ indicates that the face must contain two vertices of a $C$ommon color, a $D$ that it must contain two vertices of a $D$ifferent color and a $B$ that $B$oth conditions must hold simultaneously. A coloring of the vertices of $G$ satisfying the facial constraints is a strict $k$-coloring if it uses exactly $k$ colors. The chromatic spectrum of $G$ is the set of all $k$ for which $G$ has a strict $k$-coloring. We show that a set of integers $S$ is the spectrum of some plane graph with face-constraints if and only if $S$ is an interval $\\{s,s+1,\\dots,t\\}$ with $1\\leq s\\leq 4$, or $S=\\{2,4,5,\\dots,t\\}$, i.e. there is a gap at 3.<\/jats:p>","DOI":"10.37236\/1588","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:08:57Z","timestamp":1578708537000},"source":"Crossref","is-referenced-by-count":11,"title":["Gaps in the Chromatic Spectrum of Face-Constrained Plane Graphs"],"prefix":"10.37236","volume":"8","author":[{"given":"Daniel","family":"Kobler","sequence":"first","affiliation":[]},{"given":"Andr\u00e9","family":"K\u00fcndgen","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2001,3,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i1n3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:18:20Z","timestamp":1579324700000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i1n3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,3,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2001,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1588","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2001,3,23]]},"article-number":"N3"}}