Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 790.05008
Autor: Erdös, Paul; Richmond, L.B.
Title: On graphical partitions. (In English)
Source: Combinatorica 13, No.1, 57-63 (1993).
Review: For even n, let p(n) denote the number of partitions of n and G(n) denote the number of graphical partitions of n. A partition \pi = (\lambda1,\lambda2,...,\lambdam) is graphical if there exists a graph with degree sequence \pi. The authors discuss progress and possible lines in enquiry on the questions of whether or not limn ––> ooG(n)/p(n) approaches 0, and prove two inequalities: limsupn ––> oo{G(n)\over P(n)} \leq .4258, liminfn ––> oon ½{G(n)\over P(n)} \geq {\pi\over\sqrt 6}.
Reviewer: D.M.Bressoud (University Park)
Classif.: * 05A17 Partitions of integres (combinatorics)
11B83 Special sequences of integers and polynomials
05C99 Graph theory
Keywords: graphical partitions
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