For an integer $k\geq 2$, a spanning tree of a graph without vertices of degree from $2$ to $k$ is called a $[2,k]$-ST of the graph. The concept of $[2,k]$-STs is a natural extension of a homeomorphically irreducible spanning tree (or HIST), which is a well-studied graph structure. In this paper, we give a new strategy for finding $[2,k]$-STs. By using the strategy, we refine or extend a known degree-sum condition for the existence of a HIST. Furthermore, we also investigate a degree-product condition for the existence of a $[2,k]$-ST.
@article{10_37236_13074,
author = {Michitaka Furuya and Shoichi Tsuchiya},
title = {A new strategy for finding spanning trees without small degree stems},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/13074},
zbl = {8097651},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13074/}
}
TY - JOUR
AU - Michitaka Furuya
AU - Shoichi Tsuchiya
TI - A new strategy for finding spanning trees without small degree stems
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/13074/
DO - 10.37236/13074
ID - 10_37236_13074
ER -
%0 Journal Article
%A Michitaka Furuya
%A Shoichi Tsuchiya
%T A new strategy for finding spanning trees without small degree stems
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/13074/
%R 10.37236/13074
%F 10_37236_13074
Michitaka Furuya; Shoichi Tsuchiya. A new strategy for finding spanning trees without small degree stems. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13074
