The paper deals with the analysis of the similarity's rate of 81 universities and other schools of university's type in EU all of which have in this consideration the same status. From each state of the European Union, three largest universities according to the number of students criterion were chosen (when such an amount of universities was existing in the considered state) and added to our database. We have used hierarchical clustering methods based on the simple join of several clusters as well as methods of explorative analysis presented by some profile diagrams in order to compare these universities. As the space analysis created in the geographical information system environment is joined here with the methods of mathematical statistics, we consider the paper being important both from the interdisciplinary and the statistical-environment analysis point of view. It points out to the fact that multi-dimensional statistical methods can be used also at interdisciplinary level.

We say that a vertex colouring $\varphi$ of a graph $G$ is nonrepetitive if there is no positive integer $n$ and a path on $2n$ vertices $v_{1}\ldots v_{2n}$ in $G$ such that the associated sequence of colours $\varphi(v_{1})\ldots\varphi(v_{2n})$ satisfy $\varphi(v_{i})=\varphi(v_{i+n})$ for all $i=1,2,\dots,n$. The minimum number of colours in a nonrepetitive vertex colouring of $G$ is the Thue chromatic number $\pi (G)$. For the case of vertex list colourings the Thue choice number $\pi_{l}(G)$ of $G$ denotes the smallest integer $k$ such that for every list assignment $L:V(G)\rightarrow 2^{\mathbb{N}}$ with minimum list length at least $k$, there is a nonrepetitive vertex colouring of $G$ from the assigned lists. Recently it was proved that the Thue chromatic number and the Thue choice number of the same graph may have an arbitrary large difference in some classes of graphs. Here we give an overview of the known results where we compare these two parameters for several families of graphs and we also give a list of open problems on this topic.

A graph $G=(V,E)$ is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite $1$-planar graphs with prescribed numbers of vertices in partite sets. Bipartite 1-planar graphs are known to have at most $3n-8$ edges, where $n$ denotes the order of a graph. We show that maximal-size bipartite $1$-planar graphs which are almost balanced have not significantly fewer edges than indicated by this upper bound, while the same is not true for unbalanced ones. We prove that maximal possible sizes of bipartite $1$-planar graphs whose one partite set is much smaller than the other one tends towards $2n$ rather than $3n$. In particular, we prove that if the size of the smaller partite set is sublinear in $n$, then $|E|=(2+o(1))n$, while the same is not true otherwise.