Cubic graphs with large circumference deficit

The circumference $c(G)$ of a graph $G$ is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically $4$-, $5$- and $6$-edge-connected cubic graphs with circumference ratio $c(G)/|V(G)|$ bounded from above by $0.876$, $0.960$ and $0.990$, respectively. In contrast, the dominating cycle conjecture implies that the circumference ratio of a cyclically $4$-edge-connected cubic graph is at least $0.75$. In addition, we construct snarks with large girth and large circumference deficit, solving Problem 1 proposed in [J. H\"agglund and K. Markstr\"om, On stable cycles and cycle double covers of graphs with large circumference, Disc. Math. 312 (2012), 2540--2544]

Circular edge-colorings of cubic graphs with girth six

We show that the circular chromatic index of a (sub)cubic graph with girth at least six is at most 7/2.Comment: 13 pages, 6 figure

Zrušovanie rozhodnutí všeobecných súdov v konaní pred Ústavným súdom Slovenskej republiky

V čísle III/1996 Časopisu pro právní vědu a praxi zaujala studia V. Kratochvíla: K procesnímu postupu obecného soudu pro rozhodnutí v trestní věci nálezem Ústavního soudu České republiky.The amendment of Law No. 38/1993 Coll. on the Constitutional Court of the Slovak Republic, on the legal proceedings and on the standing of judges enforced by Law No. 293/1995 Coll. created - according to the preliminary inspection - a legal possibility that the Constitutional Court can abolish any judgement pronounced in criminal or civil proceedings.This situation may occur on the basis of a natural or fictitious person's initiative having objected an interference with constitutionalism ("interference with civil rights under the Article 130 Section 3 of the Constitution of the Slovak Republic").However, realization of this possiblity depends on how the Constitutional Court will use the new regulation and how the regulation actually affects its jurispruden­ce

Quantitative analysis of the competitiveness of Benelux countries

International audienceEconomic competitiveness is not only a microeconomic problem for business management. It is also an important indicator of comparison among the economic development, advancement and sustainability of respective countries. The investigation of macroeconomic competitiveness of individual states is at the forefront of the discourse of both macroeconomic experts and politicians. In this study we focus on the economic competitiveness of the BENELUX countries, that is Belgium, the Netherlands and Luxemburg. The objective of the article is to identify the position of the BENELUX countries as an economic union with respect to global economy and the potential for the growth and sustainability of BENELUX economic competitiveness. The first part of the article addresses the theoretical principles of the given problematic, delineates competitiveness within its economic determinants and positions a discussion with specific focus on the BENELUX countries. The article also addresses the cooperation within the union of these states in terms of sustainability of competitiveness. The empirical part of the article analyses the competitiveness of the chosen states using standard macroeconomic methods. Three indices were utilised in the analysis, the Global Competitiveness Index (GCI), the ʻDoing Businessʼ index created by the World Bank, and the Economic Freedom Index (EFI). We have also subjected the selected indicators to a correlational analysis, the aim of which was to identify possible correlations between the chosen competitiveness index and a chosen parameter. The results of the analysis reveal the current economic position of the BENELUX countries, and outline the economic opportunities and threats to further development