Type of Publication: Conference Proceedings
Authors: Zvi Lotker, D.Majumdar, N.S.Narayanaswamy, I.Weber
Title: Sequences characterizing k-Trees
ConferenceName: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Publication: Computing and Combinatorics. 12th Annual International Conference, COCOON 2006. Proceedings (Lecture Notes in Computer Science Vol.4112)
Year: 2006
Volume: 4112 NCS
Pages: 216 - 225
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. © Springer-Verlag Berlin Heidelberg 2006.
Keywords: Boolean functions;Computational geometry;Probabilistic logics;Functions;Data processing;Computational methods; ,
Last Updated: 9/4/2007 12:00:00 AM
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