A neighborhood union condition for the existence of a spanning tree without samll degree vertices

Fuente: arXiv
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Autori principali: Li, Yibo, Dong, Fengming, Liu, Huiqing
Natura: Preprint
Pubblicazione: 2025
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author Li, Yibo
Dong, Fengming
Liu, Huiqing
author_facet Li, Yibo
Dong, Fengming
Liu, Huiqing
contents For an integer k\ge2, a [2,k]-ST of a connected graph G is a spanning tree of G in which there are no vertices of degree between 2 and k. A [2,k]-ST is a natural extension of a homeomorphically irreducible spanning tree (HIST), which is a spanning tree without vertices of degree 2. In this paper, we give a neighborhood union condition for the existence of a [2,k]-ST in G. We generalize a known degree sum condition that guarantees the existence of a [2,k]-ST in G.
format Preprint
id arxiv_https___arxiv_org_abs_2510_07655
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A neighborhood union condition for the existence of a spanning tree without samll degree vertices
Li, Yibo
Dong, Fengming
Liu, Huiqing
Combinatorics
05C05
For an integer k\ge2, a [2,k]-ST of a connected graph G is a spanning tree of G in which there are no vertices of degree between 2 and k. A [2,k]-ST is a natural extension of a homeomorphically irreducible spanning tree (HIST), which is a spanning tree without vertices of degree 2. In this paper, we give a neighborhood union condition for the existence of a [2,k]-ST in G. We generalize a known degree sum condition that guarantees the existence of a [2,k]-ST in G.
title A neighborhood union condition for the existence of a spanning tree without samll degree vertices
topic Combinatorics
05C05
url https://arxiv.org/abs/2510.07655