A remark on branch weights in countable trees

Zelinka, Bohdan. "A remark on branch weights in countable trees." Mathematica Bohemica 129.1 (2004): 29-31. <http://eudml.org/doc/249400>.

@article{Zelinka2004,
abstract = {Let $T$ be a tree, let $u$ be its vertex. The branch weight $b(u)$ of $u$ is the maximum number of vertices of a branch of $T$ at $u$. The set of vertices $u$ of $T$ in which $b(u)$ attains its minimum is the branch weight centroid $B(T)$ of $T$. For finite trees the present author proved that $B(T)$ coincides with the median of $T$, therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.},
author = {Zelinka, Bohdan},
journal = {Mathematica Bohemica},
keywords = {branch weight; branch weight centroid; tree; path; degree of a vertex; branch weight centroid; tree; path; degree of a vertex},
language = {eng},
number = {1},
pages = {29-31},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on branch weights in countable trees},
url = {http://eudml.org/doc/249400},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Zelinka, Bohdan
TI - A remark on branch weights in countable trees
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 1
SP - 29
EP - 31
AB - Let $T$ be a tree, let $u$ be its vertex. The branch weight $b(u)$ of $u$ is the maximum number of vertices of a branch of $T$ at $u$. The set of vertices $u$ of $T$ in which $b(u)$ attains its minimum is the branch weight centroid $B(T)$ of $T$. For finite trees the present author proved that $B(T)$ coincides with the median of $T$, therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.
LA - eng
KW - branch weight; branch weight centroid; tree; path; degree of a vertex; branch weight centroid; tree; path; degree of a vertex
UR - http://eudml.org/doc/249400
ER -