Bounding mean orders of sub-$k$-trees of $k$-trees
Combinatorics
2024-04-09 v1
Abstract
For a -tree , we prove that the maximum local mean order is attained in a -clique of degree and that it is not more than twice the global mean order. We also bound the global mean order if has no -cliques of degree and prove that for large order, the -star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub--trees of -trees.
Cite
@article{arxiv.2309.16545,
title = {Bounding mean orders of sub-$k$-trees of $k$-trees},
author = {Stijn Cambie and Bradley McCoy and Stephan Wagner and Corrine Yap},
journal= {arXiv preprint arXiv:2309.16545},
year = {2024}
}
Comments
20 Pages, 6 Figures