{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:03Z","timestamp":1753893783878,"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>In this paper we show that for a given $k$-tree $T$ with a $k$-clique $C$, the local mean order of all sub-$k$-trees of $T$ containing $C$ is not less than the global mean order of all sub-$k$-trees of $T$, and the path-type $k$-trees have the smallest global mean sub-$k$-tree order among all $k$-trees of a given order. These two results give solutions to two problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees. Furthermore, the mean sub-$k$-tree order as a function on $k$-trees is shown to be monotone with respect to inclusion. This generalizes Jamison's result for the case $k=1$ [J. Combin. Theory Ser. B 35 (1983), 207-223].<\/jats:p>","DOI":"10.37236\/11280","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T16:32:10Z","timestamp":1678379530000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Local and Global Mean Orders of Sub-$k$-Trees of $k$-Trees"],"prefix":"10.37236","volume":"30","author":[{"given":"Zuwen","family":"Luo","sequence":"first","affiliation":[]},{"given":"Kexiang","family":"Xu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,3,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i1p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T16:32:11Z","timestamp":1678379531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i1p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/11280","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,3,10]]},"article-number":"P1.43"}}