Kellerman, RuaanZanardo, AlbertoGoranko, Valentin2024-07-252024-07-252023-12Kellerman, R., Zanardo, A., goranko, V. 2023, 'Structural theory of trees. II. Completeness and completions of trees', Contributions to Discrete Mathematics, vol. 18, no. 2, pp. 210-233.1715-0868http://hdl.handle.net/2263/97233Trees are partial orderings where every element has a linearly ordered set of smaller elements. We define and study several natural notions of completeness of trees, extending Dedekind completeness of linear orders and Dedekind-MacNeille completions of partial orders. We then define constructions of tree completions that extend any tree to a minimal one satisfying the respective completeness property.en© University of Calgary Press.Partial orderTreeCompleteCompletionArticle