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Chain of dendrites without open supremum.

Podbrdský, Pavel; Pyrih, Pavel — 2001

Mathematica Pannonica

Chain of dendrites without retract infimum.

Podbrdskÿ, Pavel; Pyrih, Pavel — 2002

Mathematica Pannonica

Chain of dendrites without open infimum.

Podbrdský, Pavel; Pyrih, Pavel — 2002

Southwest Journal of Pure and Applied Mathematics [electronic only]

On the number of intersections of two polygons

Jakub Černý; Jan Kára; Daniel Kráľ; Pavel Podbrdský; Miroslava Sotáková; Robert Šámal — 2003

Commentationes Mathematicae Universitatis Carolinae

We study the maximum possible number $f (k, l)$ of intersections of the boundaries of a simple $k$ -gon with a simple $l$ -gon in the plane for $k, l \geq 3$ . To determine the number $f (k, l)$ is quite easy and known when $k$ or $l$ is even but still remains open for $k$ and $l$ both odd. We improve (for $k \leq l$ ) the easy upper bound $k l - l$ to $k l - ⌈k / 6⌉ - l$ and obtain exact bounds for $k = 5$ $(f (5, l) = 4 l - 2)$ in this case.

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