Aequationes mathematicae

, Volume 90, Issue 3, pp 625–645 | Cite as

The height of multiple edge plane trees

  • Clemens Heuberger
  • Helmut Prodinger
  • Stephan Wagner
Open Access


Multi-edge trees as introduced in a recent paper of Dziemiańczuk are plane trees where multiple edges are allowed. We first show that d-ary multi-edge trees where the out-degrees are bounded by d are in bijection with classical d-ary trees. This allows us to analyse parameters such as the height. The main part of this paper is concerned with multi-edge trees counted by their number of edges. The distribution of the number of vertices as well as the height are analysed asymptotically.


Multi-edge tree Plane tree d-ary tree Height Limit distributions 

Mathematics Subject Classification

05A16 05A15 05C05 60C05 


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institut für MathematikAlpen-Adria-Universität KlagenfurtKlagenfurtAustria
  2. 2.Department of Mathematical SciencesStellenbosch UniversityStellenboschSouth Africa

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