We determine the maximum distance between any two of the center, centroid, and subtree core among trees with a given order. Corresponding results are obtained for trees with given maximum degree and also for trees with given diameter. The problem of the maximum distance between the centroid and the subtree core among trees with given order and diameter becomes difficult. It can be solved in terms of the problem of minimizing the number of root-containing subtrees in a rooted tree of given order and height. While the latter problem remains unsolved, we provide a partial characterization of the extremal structure.
@article{10_37236_6408,
author = {Heather Smith and L\'aszl\'o Sz\'ekely and Hua Wang and Shuai Yuan},
title = {On different ``middle parts'' of a tree},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {3},
doi = {10.37236/6408},
zbl = {1393.05081},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6408/}
}
TY - JOUR
AU - Heather Smith
AU - László Székely
AU - Hua Wang
AU - Shuai Yuan
TI - On different ``middle parts'' of a tree
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/6408/
DO - 10.37236/6408
ID - 10_37236_6408
ER -
%0 Journal Article
%A Heather Smith
%A László Székely
%A Hua Wang
%A Shuai Yuan
%T On different ``middle parts'' of a tree
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6408/
%R 10.37236/6408
%F 10_37236_6408
Heather Smith; László Székely; Hua Wang; Shuai Yuan. On different ``middle parts'' of a tree. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6408
