Document Type
Article
Publication Date
2013
Publication Title
Electronic Journal of Combinatorics
ISSN
1077-8926
Abstract
Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-, ... highest degrees to the root's neighbors, and so on.
They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent results on distance-based graph invariants.
We obtain a number of corollaries from this fact and also prove analogous results for related invariants, most notably the number of antichains of given cardinality in a rooted tree.
Recommended Citation
Andriantiana, Eric Ould Dadah, Stephan G. Wagner, Hua Wang.
2013.
"Greedy Trees, Subtrees and Antichains."
Electronic Journal of Combinatorics, 20 (3): 1-25.
source: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p28
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/221
Comments
The Electronic Journal of Combinatorics is an open access journal in which the author maintains the copyright. Article obtained from The Electronic Journal of Combinatorics.