{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:07Z","timestamp":1753893847958,"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>We prove that a $k$-tree can be viewed as a subgraph of a special type of $(k+1)$-tree that corresponds to a stacked polytope and that these \"stacked'' $(k+1)$-trees admit representations by orthogonal spheres in $\\mathbb{R}^{k+1}$. As a result, we derive lower bounds for Colin de Verdi\u00e8re's $\\mu$ of complements of partial $k$-trees and prove that $\\mu(G) + \\mu(\\overline{G}) \\geq |G| - 2$ for all chordal $G$.<\/jats:p>","DOI":"10.37236\/4444","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:10:07Z","timestamp":1578694207000},"source":"Crossref","is-referenced-by-count":2,"title":["Sphere Representations, Stacked Polytopes, and the Colin de Verdi\u00e8re Number of a Graph"],"prefix":"10.37236","volume":"23","author":[{"given":"Lon","family":"Mitchell","sequence":"first","affiliation":[]},{"given":"Lynne","family":"Yengulalp","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,1,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:05Z","timestamp":1579239425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/4444","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,1,22]]},"article-number":"P1.9"}}