Translator Disclaimer
June, 2021 Spanning Trees with Few Peripheral Branch Vertices
Pham Hoang Ha, Dang Dinh Hanh, Nguyen Thanh Loan
Author Affiliations +
Taiwanese J. Math. 25(3): 435-447 (June, 2021). DOI: 10.11650/tjm/201201


Let $T$ be a tree, a vertex of degree one is a leaf of $T$ and a vertex of degree at least three is a branch vertex of $T$. The set of leaves of $T$ is denoted by $L(T)$ and the set of branch vertices of $T$ is denoted by $B(T)$. For two distinct vertices $u$, $v$ of $T$, let $P_T[u,v]$ denote the unique path in $T$ connecting $u$ and $v$. Let $T$ be a tree with $B(T) \neq \emptyset$, for each vertex $x \in L(T)$, set $y_x \in B(T)$ such that $(V(P_T[x,y_x]) \setminus \{y_x\}) \cap B(T) = \emptyset$. We delete $V(P_T[x,y_x]) \setminus \{y_x\}$ from $T$ for all $x \in L(T)$. The resulting graph is a subtree of $T$ and is denoted by $\operatorname{R\_Stem}(T)$. It is called the reducible stem of $T$. A leaf of $\operatorname{R\_Stem}(T)$ is called a peripheral branch vertex of $T$. In this paper, we give some sharp sufficient conditions on the independence number and the degree sum for a graph $G$ to have a spanning tree with few peripheral branch vertices.

Funding Statement

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.04-2018.03.


A part of work was completed during a stay of the first named author at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank this institution for financial support and hospitality.


Download Citation

Pham Hoang Ha. Dang Dinh Hanh. Nguyen Thanh Loan. "Spanning Trees with Few Peripheral Branch Vertices." Taiwanese J. Math. 25 (3) 435 - 447, June, 2021.


Received: 14 August 2020; Revised: 20 November 2020; Accepted: 29 November 2020; Published: June, 2021
First available in Project Euclid: 9 December 2020

Digital Object Identifier: 10.11650/tjm/201201

Primary: 05C05, 05C07, 05C69

Rights: Copyright © 2021 The Mathematical Society of the Republic of China


Vol.25 • No. 3 • June, 2021
Back to Top