Spanning trees whose stems are spiders
type: Item
instance of: scholarly article
title: Spanning trees whose stems are spiders
zbMATH Open document ID: 1330.05041
author: Mikio Kano
author: Zheng Yan
published in: Graphs and Combinatorics
publication date: 2015-12-17T00:00:00Z
review text: The stem of a tree \(T\) is the graph obtained from \(T\) be deleting its leaves; a spider is a tree with at most one vertex with degree greater than two. Let \(G\) be a graph; it is proved here that if the minimal degree sum of four vertices of \(G\), such that the distance between any two of them is at least four, is at least \(|G|-5\), then \(G\) has a spanning tree whose stem is a spider. A counterexample shows that this condition is optimal. As a corollary, if the minimal degree of vertices of \(|G|\) is at least \((|G|-5)/4\), then \(G\) has a spannign tree whose stem is a spider.
reviewed by: Loïc Foissy
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 6521749
zbMATH Keywords: spanning tree
zbMATH Keywords: spider
zbMATH Keywords: stem
MaRDI profile type: Publication
full work available at URL: s00373-015-1618-2
OpenAlex ID: W1150523951
cites work: Spanning spiders and light-splitting switches
cites work: Spanning trees with at most 3 leaves in \(K_{1,4}\)-free graphs
cites work: Spanning trees with a bounded number of branch vertices in a claw-free graph
cites work: Factors and factorizations of graphs. Proof techniques in factor theory
DOI: 10.1007/S00373-015-1618-2
Recommended article: Spanning trees in a cactus
Recommended article: Spanning Trees with Many Leaves
Recommended article: Spanning trees with many leaves
Recommended article: Q4982929
Recommended article: Q4945509
Recommended article: Spanning trees with few leaves
Recommended article: Spanning Trees with Few Branch Vertices
Recommended article: Spanning trees whose stems have a bounded number of branch vertices
Recommended article: Q3131709
description: scientific article; zbMATH DE number 6521749