{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T06:34:03Z","timestamp":1780382043879,"version":"3.54.1"},"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>A chromatic root is a root of the chromatic polynomial of a graph. \u00a0Any chromatic root is an algebraic integer. Much is known about\u00a0the location of chromatic roots in the real and complex numbers, but\u00a0rather less about their properties as algebraic numbers. This question\u00a0was the subject of a seminar at the Isaac Newton Institute in late 2008. \u00a0The purpose of this paper is to report on the seminar and subsequent developments.We conjecture that, for every algebraic integer $\\alpha$, there is a natural number n such that $\\alpha+n$ is a chromatic root. This is proved\u00a0for quadratic integers; an extension to cubic integers has been found by\u00a0Adam Bohn. The idea is to consider certain special classes of graphs\u00a0for which the chromatic polynomial is a product of linear factors and one \"interesting\" factor of larger degree. We also\u00a0report computational results on the Galois groups of irreducible factors\u00a0of the chromatic polynomial for some special graphs. Finally, extensions to the Tutte polynomial are mentioned briefly.<\/jats:p>","DOI":"10.37236\/6578","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T14:25:47Z","timestamp":1578666347000},"source":"Crossref","is-referenced-by-count":3,"title":["Algebraic Properties of Chromatic Roots"],"prefix":"10.37236","volume":"24","author":[{"given":"Peter J.","family":"Cameron","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kerri","family":"Morgan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2017,2,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T00:05:36Z","timestamp":1579219536000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/6578","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,3]]},"article-number":"P1.21"}}