In this paper, we provide complete classification of classes of bipartite graphs defined by a single forbidden induced bipartite subgraph with respect to bounded/unbounded clique-width.

The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see [5,6,18]. However, the conjecture of ...

Let an edge cut partition the vertex set of the n-cube into k subsets A1, ..., Ak with ||Ai| − |Aj || ≤ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form k = 2a ± 2b with a ≥ b ≥ 0.

We propose a new similarity-based technique for declustering data. The proposed method can adapt to available information about query distributions, data distributions, data sizes and partition-size constraints. The method is based on max-cut partitioning of a similarity graph deened over the given set of data, under constraints on the partition sizes. It maximizes the chances that a pair of da...

1. Max-3-SAT: In this case, Γ represents the OR-predicate. 2. Max-Cut: We can model this as a CSP where the vertices that get assigned to one side get 0 value and the other gets 1; so the domain set is D = {0, 1}. The set Γ contains only 6= predicate. 3. Max-E3-LIN2: The domain is {0, 1}. There are two types of precidates in Γ, i.e. xi + xj + xk = 0 and xi + xj = xk = 1 (under modolu two.) 4. M...

In this work, we present a theoretical study about NP-hard optimization problems of cuts in graphs and the state of the art in approximation algorithms that use techniques of mathematical programming and of metric spaces. Three problems of cuts in graphs were modeled by integer mathematical programs and they are relaxed to admit solutions with continuous values. The solution of these programs d...

Cut-elimination is one of the most important techniques in proof theory. Roughly speaking, eliminating cuts from a proof generates a new proof without lemmas, which essentially consists of the syntactic material of the proven theorem. Traditionally cutelimination served the purpose to show consistency of calculi and thus played a central role in metamathematics. In this traditional context the ...

We investigate the approximability properties of several weighted problems, by comparing them with the respective unweighted problems. For an appropriate (and very general) definition of niceness, we show that if a nice weighted problem is hard to approximate within r, then its polynomially bounded weighted version is hard to approximate within r − o(1). Then we turn our attention to specific p...