Paper Info
Title
On the number of hypercubic bipartitions of an integer.
Abstract
For n≤2k we study the maximum number of edges of an induced subgraph on n vertices of the k-dimensional hypercube Qk. In the process we revisit a well-known divide-and-conquer maximin recurrence f(n)=max(min(n1,n2)+f(n1)+f(n2)) where the maximum is taken over all proper bipartitions n=n1+n2. We first use known results to present a characterization of those bipartitions n=n1+n2 that yield the maximum f(n)=min(n1,n2)+f(n1)+f(n2). Then we use this characterization to present the main result of this article, namely, for a given n∈N, the determination of the number h(n) of these bipartitions that yield the said maximum f(n). We present recursive formulae for h(n), a generating function h(x), and an explicit formula for h(n) in terms of a special representation of n.
Year
DOI
Venue
2013
10.1016/j.disc.2013.08.033
Discrete Mathematics
Keywords
Field
DocType
Rectangular grid,Hypercube,Induced subgraphs,Bipartition,Divide-and-conquer,Divide-and-conquer maximin recurrence
Integer,Generating function,Discrete mathematics,Combinatorics,Mathematics
Journal
Volume
Issue
ISSN
313
24
0012-365X
Citations 
PageRank 
References 
1
0.41
7
Authors
1
Name
Order
Citations
PageRank
Geir Agnarsson110314.69