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.

Convex 4-valent polytopes with prescribed types of faces

Marián Trenkler — 1984

Commentationes Mathematicae Universitatis Carolinae

On the Face-Vector of a 5-Valent Convex 3-Polytope

Marián Trenkler — 1975

Matematický časopis

On $4$ -connected, planar $4$ -almost pancyclic graphs

Marián Trenkler — 1989

Mathematica Slovaca

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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