Mathematical Sciences: Faculty Publications
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
Copyright
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.
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.