arXiv subjects
Publications and source records attributed to Zoltán Kása.
In randomly created structures (be they natural or artificial) very often there exist ordered substructures. In this Hungarian language scientific essay we will present some of such structures in graph theory. E.g. Rédei's theorem, Ramsey theory, Turán's problem, Hamiltonian cycles in De Bruijn graphs.
The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.
We give two equivalent formulations of a conjecture [2,4] on the number of arc-disjoint Hamiltonian cycles in De Bruijn graphs.
In this paper we introduce and study a new complexity measure for finite words. For positive integer $d$ special scattered subwords, called super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are defined. We give methods to compute super-$d$-complexity (the total number of different super-$d$-subwords) in the case of rainbow words (with pairwise different letters) by recursive algorithms, by mahematical formulas and by graph algorithms. In the case of general words, with letters from a given alphabet without any restriction, the problem of the maximum value of the super-$d$-complexity of all words of length $n$ is presented.
Special scattered subwords, in which the gaps are of length from a given set, are defined. The scattered subword complexity, which is the number of such scattered subwords, is computed for rainbow words.
In the paper are computed: the number of binary trees with n nodes and k leaves; the number of leaves in the set of all binary trees with n nodes. These are used to compute the number of states in the buddy system.
A coding method using binary sequences is presented for different computation problems related to Catalan numbers. This method proves in a very easy way the equivalence of these problems.