On spanning trees with high internal degree
Combinatorics
2016-07-20 v1
Abstract
Alon and Wormald showed that any graph with minimum degree d contains a spanning star forest in which every connected component is of size at least \Omega((d/\log d)^{1/3}). They asked if any connected graph with minimum degree at least d has a spanning tree in which every internal vertex has degree at least cd/\log d, for some absolute constant c > 0. We give a simple example showing that this is not the case.
Keywords
Cite
@article{arxiv.1607.05460,
title = {On spanning trees with high internal degree},
author = {Codrut Grosu},
journal= {arXiv preprint arXiv:1607.05460},
year = {2016}
}