In this paper we de1ne the vertex-cover polynomial (G; ) for a graph G. The coe2cient of r in this polynomial is the number of vertex covers V ′ of G with |V ′|= r. We develop a method to calculate (G; ). Motivated by a problem in biological systematics, we also consider the mappings f from {1; 2; : : : ; m} into the vertex set V (G) of a graph G, subject to f−1(x) ∪ f−1(y) = ∅ for every edge x...

A graph G has a planar cover if there exists a planar graph H , and a homomorphism φ : H → G that maps the neighbours of each vertex bijectively. Each graph that has an embedding in the projective plane also has a finite planar cover. Negami conjectured the converse in 1988. This conjecture holds as long as no minor-minimal non-projective graph has a finite planar cover. From the list there rem...

A subset S of vertices of a graph G = (V,E) is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from S. Denote by ψk(G) the minimum cardinality of a k-path vertex cover in G and form a sequence ψ(G) = (ψ1(G), ψ2(G), . . . , ψ|V |(G)), called the path sequence of G. In this paper we prove necessary and sufficient conditions for two integers to appear on ...

We give an O(n) algorithm to find a minimum clique cover of a (bull, C4)-free graph, or equivalently, a minimum colouring of a (bull, 2K2)-free graph, where n is the number of vertices of the graphs.

In the course of history, a large number of politicians have been assassinated. To investigate this phenomenon, rational choice hypotheses are developed and tested using a large data set covering close to 100 countries over a period of 20 years. Several strategies, in addition to security measures, are shown to significantly reduce the probability of politicians being attacked or killed: extend...

Using a longitudinal data set covering the period 1987–2000, the authors explore the impact of female employers and gender segregation on wages in Portugal. In the context of Becker’s (1957) taste for discrimination theory, they investigate whether the gender of a firm manager affects gender wage differences. They find that females benefit from higher wages in female-led firms than in male-led ...

The usefulness of a climate-model simulation cannot be inferred solely from its degree of agreement with observations. Instead, one has to consider additional factors such as internal variability, the tuning of the model, observational uncertainty, the temporal change in dominant processes or the uncertainty in the forcing. In any model-evaluation study, the impact of these limiting factors on ...

We present a reference, comprehensive, high-resolution, digital mosaic of ice motion in Antarctica assembled from multiple satellite interferometric synthetic-aperture radar data acquired during the International Polar Year 2007 to 2009. The data reveal widespread, patterned, enhanced flow with tributary glaciers reaching hundreds to thousands of kilometers inland over the entire continent. Thi...