Geodesic
On the inducibility of small trees
Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4

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The quantity that captures the asymptotic value of the maximum number of appearances of a given topological tree (a rooted tree with no vertices of outdegree $1$) $S$ with $k$ leaves in an arbitrary tree with sufficiently large number of leaves is called the inducibility of $S$. Its precise value is known only for some specific families of trees, most of them exhibiting a symmetrical configuration. In an attempt to answer a recent question posed by Czabarka, Sz\'ekely, and the second author of this article, we provide bounds for the inducibility $J(A_5)$ of the $5$-leaf binary tree $A_5$ whose branches are a single leaf and the complete binary tree of height $2$. It was indicated before that $J(A_5)$ appears to be `close' to $1/4$. We can make this precise by showing that $0.24707\ldots \leq J(A_5) \leq 0.24745\ldots$. Furthermore, we also consider the problem of determining the inducibility of the tree $Q_4$, which is the only tree among $4$-leaf topological trees for which the inducibility is unknown. 
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     title = {On the inducibility of small trees},
     journal = {Discrete mathematics & theoretical computer science},
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Dossou-Olory, Audace A. V.; Wagner, Stephan. On the inducibility of small trees. Discrete mathematics & theoretical computer science, Tome 21 (2019) no. 4. doi: 10.23638/DMTCS-21-4-13

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