{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:35Z","timestamp":1753893815560,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-,\u00a0... highest degrees to the root's neighbors, and so on.\u00a0They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent results on distance-based graph invariants.\u00a0We obtain a number of corollaries from this fact and also prove analogous results for related invariants, most notably the number of antichains of given cardinality in a rooted tree.<\/jats:p>","DOI":"10.37236\/3101","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:22:48Z","timestamp":1578705768000},"source":"Crossref","is-referenced-by-count":12,"title":["Greedy Trees, Subtrees and Antichains"],"prefix":"10.37236","volume":"20","author":[{"given":"Eric Ould Dadah","family":"Andriantiana","sequence":"first","affiliation":[]},{"given":"Stephan","family":"Wagner","sequence":"additional","affiliation":[]},{"given":"Hua","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:14:05Z","timestamp":1579259645000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/3101","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,8,30]]},"article-number":"P28"}}