On the number of hypercubic bipartitions of an integer |
| |
Authors: | Geir Agnarsson |
| |
Institution: | Department of Mathematical Sciences, George Mason University, MS 3F2, 4400 University Drive, Fairfax, VA 22030, United States |
| |
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. |
| |
Keywords: | Rectangular grid Hypercube Induced subgraphs Bipartition Divide-and-conquer Divide-and-conquer maximin recurrence |
本文献已被 ScienceDirect 等数据库收录! |
|