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.