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

Voir la notice de l'article provenant de la source Episciences

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. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-4-13/

Cité par Sources :