Global transformational processes associated with the geopolitical fragmentation of the world, changes in supply chains, and the emergence of threats to food, energy, logistics security, etc. have impacted the increase in the freight traffic volumes through the Ukraine-European Union (Ukraine-EU) land border section. In this context, the transport and logistics infrastructure on this section of the border was inadequate for the growing demand for international freight transport, leading to huge economic, social, and environmental damage to all participants in foreign trade. The aim of this paper is to study the efficiency of the functioning of the transport and logistics infrastructure on the Ukraine-EU border section. The taxonomy used in the paper made it possible to look into economic, security, geopolitical, logistics, transport, legal, and political factors shaping the freight traffic volumes, structure, and routes; their key trends and impact on the generation of freight traffic are described. Statistical analysis of freight traffic by border sections and with respect to border crossing points allowed the identification of bottlenecks in the functioning of the transport and logistics infrastructure and outlining ways to address them. The results of the study will be helpful both to researchers working on the issues of freight transport and to policymakers involved in transport and border infrastructure development.

It is well known that determining the exact values of crossing number for circulant graphs is very difficult. Even so, some important results in this field are still proved. D.J. Ma was proved that the crossing number of C(2m + 2, m) is m + 1[8]. Then such problem for C(n, 3) was further solved [7]. Pak Tung Ho and X. Lin obtained accurate values for the crossover numbers of C (3m, m) and C (3m + 1, m)[4][5]. In this paper, as a complement, we show that the edges from the principal cycle of C(9, 3) do not cross each other in an optimal drawing.