{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:31Z","timestamp":1753893811871,"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>For a $k$-tree $T$, we prove that the maximum local mean order is attained in a $k$-clique of degree $1$ and that it is not more than twice the global mean order. We also bound the global mean order if $T$ has no $k$-cliques of degree $2$ and prove that for large order, the $k$-star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees.<\/jats:p>","DOI":"10.37236\/12426","type":"journal-article","created":{"date-parts":[[2024,3,21]],"date-time":"2024-03-21T16:22:58Z","timestamp":1711038178000},"source":"Crossref","is-referenced-by-count":0,"title":["Bounding Mean Orders of Sub-$k$-Trees of $k$-Trees"],"prefix":"10.37236","volume":"31","author":[{"given":"Stijn","family":"Cambie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bradley","family":"McCoy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephan","family":"Wagner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Corrine","family":"Yap","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,3,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p62\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i1p62\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,14]],"date-time":"2024-04-14T13:46:25Z","timestamp":1713102385000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i1p62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/12426","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,3,22]]},"article-number":"P1.62"}}