{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:09Z","timestamp":1753893849690,"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>The Colin de Verdi\u00e8re\u00a0parameter $\\mu(G)$ is a minor-monotone graph parameter with connections to differential geometry. We study the conjecture that for every integer $t$, if $G$ is a graph with at least $t$ vertices and $\\mu(G) \\leq t$, then $|E(G)| \\leq t|V(G)|-\\binom{t+1}{2}$. We observe a relation to the graph complement conjecture for the Colin de Verdi\u00e8re parameter and prove the conjectured edge upper bound for graphs $G$ such that either $\\mu(G) \\leq 7$, or $\\mu(G) \\geq |V(G)|-6$, or the complement of $G$ is chordal, or $G$ is chordal.<\/jats:p>","DOI":"10.37236\/7195","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:33:14Z","timestamp":1578670394000},"source":"Crossref","is-referenced-by-count":2,"title":["The Extremal Function and Colin de Verdi\u00e8re Graph Parameter"],"prefix":"10.37236","volume":"25","author":[{"given":"Rose","family":"McCarty","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,5,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p32\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i2p32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:33:35Z","timestamp":1579235615000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i2p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,25]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2018,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7195","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,5,25]]},"article-number":"P2.32"}}