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arXiv · 1601.07149

Inducibility in binary trees and crossings in random tanglegrams

Éva Czabarka·László A. Székely·Stephan Wagner
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Abstract

In analogy to other concepts of a similar nature, we define the inducibility of a rooted binary tree. Given a fixed rooted binary tree $B$ with $k$ leaves, we let $γ(B,T)$ be the proportion of all subsets of $k$ leaves in $T$ that induce a tree isomorphic to $B$. The inducibility of $B$ is $\limsup_{|T| \to \infty} γ(B,T)$. We determine the inducibility in some special cases, show that every binary tree has positive inducibility and prove that caterpillars are the only binary trees with inducibility $1$. We also formulate some open problems and conjectures on the inducibility. Finally, we present an application to crossing numbers of random tanglegrams.

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Éva Czabarka, László A. Székely, Stephan Wagner. 2016-01-26. Inducibility in binary trees and crossings in random tanglegrams. https://arxiv.org/abs/1601.07149

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