Counting Planar Tanglegrams

Authors Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana, Stephan Wagner

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Author Details

Dimbinaina Ralaivaosaona
  • Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa
Jean Bernoulli Ravelomanana
  • Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa
Stephan Wagner
  • Department of Mathematical Sciences, Stellenbosch University, Stellenbosch, South Africa

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Dimbinaina Ralaivaosaona, Jean Bernoulli Ravelomanana, and Stephan Wagner. Counting Planar Tanglegrams. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 32:1-32:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Tanglegrams are structures consisting of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the two trees. We say that a tanglegram is planar if it can be drawn in the plane without crossings. Using a blend of combinatorial and analytic techniques, we determine an asymptotic formula for the number of planar tanglegrams with n leaves on each side.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Enumeration
  • Mathematics of computing → Generating functions
  • rooted binary trees
  • tanglegram
  • planar
  • generating functions
  • asymptotic enumeration
  • singularity analysis


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