We give a construction of $p$ orthogonal Latin $p$ -dimensional cubes (or Latin hypercubes) of order $n$ for every natural number $n \neq 2, 6$ and $p \geq 2$ . Our result generalizes the well known result about orthogonal Latin squares published in 1960 by R. C. Bose, S. S. Shikhande and E. T. Parker.

70th birthday of Professor Ernest Jucovič

Marián Trenkler — 1997

Mathematica Slovaca

Characterization of magic graphs

Samuel Jezný; Marián Trenkler — 1983

Czechoslovak Mathematical Journal

On a generalization of perfect $b$ -matching

Ľubica Šándorová; Marián Trenkler — 1991

Mathematica Bohemica

The paper is concerned with the existence of non-negative or positive solutions to $A f = β$ , where $A$ is the vertex-edge incidence matrix of an undirected graph. The paper gives necessary and sufficient conditions for the existence of such a solution.

Magic powers of graphs

Marián Trenkler; Vladimír Vetchý — 1997

Mathematica Bohemica

Necessary and sufficient conditions for a graph $G$ that its power $G^{i}$ , $i \geq 2$ , is a magic graph and one consequence are given.

Constructions of triangular and quadrangular polyhedra of inscribable type

Ernest Jucovič; Sergej Ševec; Marián Trenkler — 1997

Mathematica Slovaca

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