The history of degenerate (bipartite) extremal graph problems

This paper is a survey on Extremal Graph Theory, primarily focusing on the case when one of the excluded graphs is bipartite. On one hand we give an introduction to this field and also describe many important results, methods, problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version of our survey presented in Erdos 100. In this version 2 only a citation was complete

Analysis of the main causes of traffic problems in cities

The current state of mobility in our cities is still showing worse and worse transport, security and environmental conditions. The most common problem of traffic services in cities is the inability to arrange the conditions for the transport of persons and the transport of goods and services. Inappropriate conditions are evident mainly in traffic congestion, which cause significant time losses for all users of the means of transport (mass transport of persons is not exemption). The daily practice proves that one of the crucial conditions not only for the satisfaction of the inhabitants, but also for the city’s own functionality is the high-quality, fast, safe and dynamic transport and also parking on its territory. Increasing and widespread traffic collapse in cities is caused by two factors. The first is an enormous increase in car traffic which significantly limiting other types of transport. The second is an inappropriate localization of various activities and facilities. Unregulated urban development is caused by disregarding the landuse plan and cities have unregulated construction. This results in inadequate traffic requirements in specific areas, which significantly exceed the capacities of transport communications. In our papers are described mentioned problems and, as a deterrent example, we introduce the city of Žilina