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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