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.
@article{DMTCS_2019_21_4_a14,
author = {Dossou-Olory, Audace A. V. and Wagner, Stephan},
title = {On the inducibility of small trees},
journal = {Discrete mathematics & theoretical computer science},
publisher = {mathdoc},
volume = {21},
number = {4},
year = {2019},
doi = {10.23638/DMTCS-21-4-13},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-13/}
}
TY - JOUR AU - Dossou-Olory, Audace A. V. AU - Wagner, Stephan TI - On the inducibility of small trees JO - Discrete mathematics & theoretical computer science PY - 2019 VL - 21 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-13/ DO - 10.23638/DMTCS-21-4-13 LA - en ID - DMTCS_2019_21_4_a14 ER -
%0 Journal Article %A Dossou-Olory, Audace A. V. %A Wagner, Stephan %T On the inducibility of small trees %J Discrete mathematics & theoretical computer science %D 2019 %V 21 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-13/ %R 10.23638/DMTCS-21-4-13 %G en %F DMTCS_2019_21_4_a14
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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