Spanning trees without adjacent vertices of degree 2
Combinatorics
2019-01-11 v2
Abstract
Albertson, Berman, Hutchinson, and Thomassen showed in 1990 that there exist highly connected graphs in which every spanning tree contains vertices of degree 2. Using a result of Alon and Wormald, we show that there exists a natural number such that every graph of minimum degree at least contains a spanning tree without adjacent vertices of degree 2. Moreover, we prove that every graph with minimum degree at least 3 has a spanning tree without three consecutive vertices of degree 2.
Keywords
Cite
@article{arxiv.1801.07025,
title = {Spanning trees without adjacent vertices of degree 2},
author = {Kasper Szabo Lyngsie and Martin Merker},
journal= {arXiv preprint arXiv:1801.07025},
year = {2019}
}