The bipartite density of a graphG is max{|E(H)|/|E(G)| : H is a bipartite subgraph of G}. It is NP-hard to determine the bipartite density of any triangle-free cubic graph. A biased maximum bipartite subgraph of a graph G is a bipartite subgraph of G with the maximum number of edges such that one of its partite sets is independent in G. Let H denote the collection of all connected cubic graphs ...

In supervised learning, discretization of the continuous explanatory attributes enhances the accuracy of decision tree induction algorithms and naive Bayes classifier. Many discretization methods have been developped, leading to precise and comprehensible evaluations of the amount of information contained in one single attribute with respect to the target one. In this paper, we discuss the mult...

The vertex set of a halved cube Qd consists of a bipartition vertex set of a cube Qd and two vertices are adjacent if they have a common neighbour in the cube. Let d ≥ 5. Then it is proved that Qd is the only connected, ( d 2 ) -regular graph on 2d−1 vertices in which every edge lies in two d-cliques and two d-cliques do not intersect in a vertex.

Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that for both i = 1, 2 we have eGi(A,B) ≥ mi/2 − √ mi. This answers a question of Bollobás and Scott. We also prove results about partitions into more than two vertex classes.

A bipartition of HIV-1 RNA genome sequences into single- and double-stranded nucleotides is possible based on the secondary structure model of a complete 9 kb genome. Subsequent analysis revealed that the well-known lentiviral property of A-accumulation is profoundly present in single-stranded domains, yet absent in double-stranded domains. Mutational rate analysis by means of an unrestricted m...

In the representation theory of Iwahori–Hecke algebras of type A (and in particular for representations of symmetric groups) the notion of the weight of a block, introduced by James, plays a central rôle. Richards determined the decomposition numbers for blocks of weight 2, and here the same task is undertaken for weight two blocks of Iwahori–Hecke algebras of type B, using the author’s own def...

Let G be a connected bipartite graph. An involution α of G that preserves the bipartition of G is called bipartite. Let Gα be the graph obtained from G by adding to G the natural perfect matching induced by α. We show that the k-cube Qk is isomorphic to the direct product G×H if and only if G is isomorphic to Qk−1 for some bipartite involution α of Qk−1 and H = K2.

In this work we present some matrix operators named circulant operators and their action on square matrices. This study on square matrices provides new insights into the structure of the space of square matrices. Moreover it can be useful in various fields as in agents networking on Grid or large-scale distributed self-organizing grid systems. Keywords— Pascal matrices, Binomial Recursion, Circ...

This work is devoted to a systematic investigation of triangular matrix forms of the Pascal Triangle. To start, the twelve matrix forms (collectively referred to as G-matrices) are presented. To highlight one way in which the G-matrices relate to each other, a set of four operators named circulant operators is introduced. These operators provide a new insight into the structure of the space of ...

Let G be a properly colored bipartite graph. A rainbow matching of G is such a matching in which no two edges have the same color. Let G be a properly colored bipartite graph with bipartition ( X , Y ) and . We show that if   = G k   3   7 max , 4 k X Y  , then G has a rainbow coloring of size at least 3 4 k       .