Les grammairiens hesitent cependant entre la
bipartition traditionnelle corporel vs.
(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.
Une telle
bipartition, qui rejoue celle du pouvoir villageois, entre autorites locales et simples villageois, nous apparait essentielle.
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.
