## Durant, Kevin and Wagner, Stephan - On the centroid of increasing trees

dmtcs:4325 - Discrete Mathematics & Theoretical Computer Science, August 27, 2019, vol. 21 no. 4 - https://doi.org/10.23638/DMTCS-21-4-8
On the centroid of increasing trees

Authors: Durant, Kevin and Wagner, Stephan

A centroid node in a tree is a node for which the sum of the distances to all other nodes attains its minimum, or equivalently a node with the property that none of its branches contains more than half of the other nodes. We generalise some known results regarding the behaviour of centroid nodes in random recursive trees (due to Moon) to the class of very simple increasing trees, which also includes the families of plane-oriented and $d$-ary increasing trees. In particular, we derive limits of distributions and moments for the depth and label of the centroid node nearest to the root, as well as for the size of the subtree rooted at this node.

Volume: vol. 21 no. 4
Section: Combinatorics
Published on: August 27, 2019
Submitted on: February 27, 2018
Keywords: Mathematics - Combinatorics