Sequences characterizing k-Trees

Zvi Lotker, Debapriyo Majumdar, N. S. Narayanaswamy, Ingmar Weber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

A non-decreasing sequence of n integers is the degree sequence of a 1-tree (i.e., an ordinary tree) on n vertices if and only if there are least two 1's in the sequence, and the sum of the elements is 2(n - 1). We generalize this result in the following ways. First, a natural generalization of this statement is a necessary condition for k-trees, and we show that it is not sufficient for any k > 1. Second, we identify non-trivial sufficient conditions for the degree sequences of 2-trees. We also show that these sufficient conditions are almost necessary using bounds on the partition function p(n) and probabilistic methods. Third, we generalize the characterization of degrees of 1-trees in an elegant and counter-intuitive way to yield integer sequences that characterize k-trees, for all k.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 12th Annual International Conference, COCOON 2006, Proceedings
PublisherSpringer Verlag
Pages216-225
Number of pages10
ISBN (Print)3540369252, 9783540369257
DOIs
StatePublished - 1 Jan 2006
Externally publishedYes
Event12th Annual International Conference on Computing and Combinatorics, COCOON 2006 - Taipei, Taiwan, Province of China
Duration: 15 Aug 200618 Aug 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4112 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference12th Annual International Conference on Computing and Combinatorics, COCOON 2006
Country/TerritoryTaiwan, Province of China
CityTaipei
Period15/08/0618/08/06

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