Bounding Mean Orders of Sub-k-Trees of k-Trees

For a k-tree T, we prove that the maximum local mean order is attained in a k-clique of degree $1$ and that it is not more than twice the global mean order. We also bound the global mean order if T has no k-cliques of degree $2$ and prove that for large order, the k-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-k-trees of k-trees.