Given a bipartite graph G = (X ∪̇ D, E ⊆ X × D), an Xperfect matching is a matching in G that saturates every node in X. In this paper we study the following generalisation of the X-perfect matching problem, which has applications in constraint programming: Given a bipartite graph as above and a collection F ⊆ 2 of k subsets of X, find a subset M ⊆ E of the edges such that for each C ∈ F , the e...

Pedigree graphs, which represent family relationships, are often constructed by collecting data from genealogical records to determine which pairs of people are parent and child. This process is expensive, and small mistakes in data collection–for example, one missing parent-child relationship–can cause large differences in the pedigree graphs created. In this paper, we introduce a simple pedig...

A bipartite graph G = (L,R;E) with at least one edge is said to be identifiable if for every vertex v ∈ L, the subgraph induced by its non-neighbors has a matching of cardinality |L| − 1. An `-subgraph of G is an induced subgraph of G obtained by deleting from it some vertices in L together with all their neighbors. The Identifiable Subgraph problem is the problem of determining whether a given...

Let T be a triangulation of a simple polygon. A flip in T is the operation of replacing one diagonal of T by a different one such that the resulting graph is again a triangulation. The flip distance between two triangulations is the smallest number of flips required to transform one triangulation into the other. For the special case of convex polygons, the problem of determining the shortest fl...

We consider the two problems of finding the maximum number of node disjoint triangles and edge disjoint triangles in an undirected graph. We show that the first (respectively second) problem is polynomially solvable if the maximum degree of the input graph is at most 3 (respectively 4), whereas it is APX-hard for general graphs and NP-hard for planar graphs if the maximum degree is 4 (respectiv...

In this paper we study the following problem, named Maximum Edges in Transitive Closure, which has applications in computational biology. Given a simple, undirected graph G = (V,E) and a coloring of the vertices, remove a collection of edges from the graph such that each connected component is colorful (i.e., it does not contain two identically colored vertices) and the number of edges in the t...

A new wear testing system, which carries out toothbrush wear and simulated occlusal wear tests alternately, was developed. Differences in wear behavior among three modes of wears, combined wear, toothbrush wear and simulated occlusal wear, were investigated using polymethylmethacrylate (PMMA) and two commercial resin composites (Z100, APX). The area of the material loss after each test was meas...

The study of the approximability properties of NP-hard optimization problems has recently made great advances mainly due to the results obtained in the eld of proof checking. The last important breakthrough shows the APX-completeness of several important optimization problems is proved and thus reconciles`two distinct views of approximation classes: syntactic and computational'. In this paper w...

In the Art Gallery problem a polygon is given and the goal is to place as few guards as possible so that the entire area of the polygon is covered. We address a closely related problem: how to place a fixed number of guards on the vertices or the edges of a simple polygon so that the total guarded area inside the polygon is maximized. Recall that an optimization problem is called APX-hard, if t...

Results of serotyping of 122 strains of Actinobacillus pleuropneumoniae isolated on 21 swine farms in the Czech Republic from January 1999 to December 2000 are presented. The highest prevalence was found for serotype 9 (n = 81, 66.4%), followed by serotype 2 (n = 19, 15.7%). Serotypes 1, 3, 5, 7, 8, 11, and 12 were identified only sporadically. Twenty-six of the isolates were tested for gene-to...