The relation between the number of leaves of a tree and its diameter

Qiao, Pu, and Zhan, Xingzhi. "The relation between the number of leaves of a tree and its diameter." Czechoslovak Mathematical Journal 72.2 (2022): 365-369. <http://eudml.org/doc/298316>.

@article{Qiao2022,
abstract = {Let $L(n,d)$ denote the minimum possible number of leaves in a tree of order $n$ and diameter $d.$ Lesniak (1975) gave the lower bound $B(n,d)=\lceil 2(n-1)/d\rceil $ for $L(n,d).$ When $d$ is even, $B(n,d)=L(n,d).$ But when $d$ is odd, $B(n,d)$ is smaller than $L(n,d)$ in general. For example, $B(21,3)=14$ while $L(21,3)=19.$ In this note, we determine $L(n,d)$ using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.},
author = {Qiao, Pu, Zhan, Xingzhi},
journal = {Czechoslovak Mathematical Journal},
keywords = {leaf; diameter; tree; spider},
language = {eng},
number = {2},
pages = {365-369},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The relation between the number of leaves of a tree and its diameter},
url = {http://eudml.org/doc/298316},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Qiao, Pu
AU - Zhan, Xingzhi
TI - The relation between the number of leaves of a tree and its diameter
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 2
SP - 365
EP - 369
AB - Let $L(n,d)$ denote the minimum possible number of leaves in a tree of order $n$ and diameter $d.$ Lesniak (1975) gave the lower bound $B(n,d)=\lceil 2(n-1)/d\rceil $ for $L(n,d).$ When $d$ is even, $B(n,d)=L(n,d).$ But when $d$ is odd, $B(n,d)$ is smaller than $L(n,d)$ in general. For example, $B(21,3)=14$ while $L(21,3)=19.$ In this note, we determine $L(n,d)$ using new ideas. We also consider the converse problem and determine the minimum possible diameter of a tree with given order and number of leaves.
LA - eng
KW - leaf; diameter; tree; spider
UR - http://eudml.org/doc/298316
ER -