The article deals with the questions of the (in)visibility of women in Slovak political life. The material presents statistical data on women's participation in Slovak national, regional and local politics with the support of qualitative data from interviews with women politicians and activists. The author looks at the reasons for the low political representation of women and the unsuccessful attempts to increase it by introducing positive mechanisms such as quotas. The primary focus is put on the representation of women in municipal politics. The author analyses the main reasons why women are more successful in local politics than in 'high' politics.
The k-core of a graph G, Ck(G), is the maximal induced subgraph H ⊆ G such that δ(G) ≥ k, if it exists. For k > 0, the k-shell of a graph G is the subgraph of G induced by the edges contained in the k-core and not contained in the (k + 1)-core. The core number of a vertex is the largest value for k such that v ∈ Ck(G), and the maximum core number of a graph, Cb(G), is the maximum of the core numbers of the vertices of G. A graph G is k-monocore if Cb(G) = δ(G) = k. This paper discusses some basic results on the structure of k-cores and k-shells. In particular, an operation characterization of 2-monocore graphs is proven. Some applications of cores and shells to graph coloring and domination are considered.