{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:33Z","timestamp":1753893813350,"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>A connected $k$-chromatic graph $G$ is said to be double-critical if for all edges $uv$ of $G$ the graph $G - u - v$ is $(k-2)$-colourable. A longstanding conjecture of Erd\u0151s and Lov\u00e1sz states that the complete graphs are the only double-critical graphs. Kawarabayashi, Pedersen and Toft [Electron. J. Combin., 17(1): Research Paper 87, 2010] proved that every double-critical $k$-chromatic graph with $k \\leq 7$ contains a $K_k$ minor. It remains unknown whether an arbitrary double-critical $8$-chromatic graph contains a $K_8$ minor, but in this paper we prove that any double-critical $8$-chromatic contains a minor isomorphic to $K_8$ with at most one edge missing. In addition, we observe that any double-critical $8$-chromatic graph with minimum degree different from $10$ and $11$ contains a $K_8$ minor.<\/jats:p>","DOI":"10.37236\/567","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:51:31Z","timestamp":1578696691000},"source":"Crossref","is-referenced-by-count":5,"title":["Complete and Almost Complete Minors in Double-Critical $8$-Chromatic Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Anders Sune","family":"Pedersen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,4,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p80\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p80\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T18:14:28Z","timestamp":1579284868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p80"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/567","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,7]]},"article-number":"P80"}}