(6.) The expression `super-set' is used here to indicate that the possibility of representing the marriage network by means of a bipartite graph (see Hage and Harary 1991) does not, in itself, imply the existence of such
bipartitions as culturally recognised units.
In this paper, we investigate the restricted
bipartition function [c.sub.N] (n) for n = 7, 11, and 5l, for any integer l [greater than or equal to] 1, and prove some congruence properties modulo 2, 3, and 5 by using Ramanujan's theta-function identities.
Proof: We use the terminology introduced above to deal with the
bipartition of G and its specific vertex a all along this proof.
Let H be the bipartite graph with
bipartition (A, B) where A = [V.sub.1] [union] [V.sub.2] [union] ...
A perfect diagonalization of a bipartite (4,6)-fullerene B is a diagonalization in which all vertices chosen are in the same class of the
bipartition.
La
bipartition entre un carnaval blanc et un carnaval afro-americain ne suffit pas non plus a l'analyse.
Let G be a bipartite graph with
bipartition (X, Y), where X = {[x.sub.0], [x.sub.1],...
The cut-rank function [[rho].sub.G] of a graph G is defined as follows: For a
bipartition (U, W) of the vertex set V (G), [[rho].sub.G](U) = [[rho].sub.G](W) equals the rank of [A.sub.G][U,W] over GF(2).
The partitioning problem is to find a
bipartition P, where P =([V.sub.h], [V.sub.s]) such that [V.sub.h] [union] [V.sub.s] = V and [V.sub.h] [intersection] [V.sub.s] = 0.
Asano, Bhattacharya, Keil and Yao [25] later gave optimal O (n log n) algorithm using maximum spanning trees for minimizing the maximum diameter of a
bipartition. Asano, Bhattacharya, Keil and Yao also considered the clustering problem in which the goal to maximize the minimum inter-cluster distance.
