Sequences characterizing k-Trees

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages216-225
Number of pages10
Volume4112 LNCS
Publication statusPublished - 16 Oct 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)03029743
ISSN (Electronic)16113349

Other

Other12th Annual International Conference on Computing and Combinatorics, COCOON 2006
CountryTaiwan, Province of China
CityTaipei
Period15/8/0618/8/06

Fingerprint

K-tree
Degree Sequence
Integer Sequences
Generalise
Probabilistic Methods
Sufficient Conditions
Partition Function
Intuitive
Sufficient
If and only if
Necessary Conditions
Integer
Necessary

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Lotker, Z., Majumdar, D., Narayanaswamy, N. S., & Weber, I. (2006). Sequences characterizing k-Trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4112 LNCS, pp. 216-225). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS).

Sequences characterizing k-Trees. / Lotker, Zvi; Majumdar, Debapriyo; Narayanaswamy, N. S.; Weber, Ingmar.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS 2006. p. 216-225 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4112 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Lotker, Z, Majumdar, D, Narayanaswamy, NS & Weber, I 2006, Sequences characterizing k-Trees. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 4112 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4112 LNCS, pp. 216-225, 12th Annual International Conference on Computing and Combinatorics, COCOON 2006, Taipei, Taiwan, Province of China, 15/8/06.
Lotker Z, Majumdar D, Narayanaswamy NS, Weber I. Sequences characterizing k-Trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS. 2006. p. 216-225. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Lotker, Zvi ; Majumdar, Debapriyo ; Narayanaswamy, N. S. ; Weber, Ingmar. / Sequences characterizing k-Trees. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4112 LNCS 2006. pp. 216-225 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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