E. Makai

activity

19992021

most citedVolume product of planar polar convex bodies --- lower estimates with stability

5 citations · 17 across the 20 of their papers we have counts for

collaborators

22 papers

math.CO2021

Nearly equal distances in the plane, II

P. Erdős, E. Makai, J. Pach

Let ${p_{1}, \dots, p_{n}} \subset R^{2}$ be a separated point set, i.e., any two points have a distance at least $1$ . Let $k \geq 1$ be an integer, and $1 \le t_1 < \ldots <…

math.CO2021

On the number of antipodal or strictly antipodal pairs of points in finite subsets of $R^{d}$ , III

E. Makai, H. Martini, M. H. Nguyên +2

We improve our earlier upper bound on the numbers of antipodal pairs of points among $n$ points in $R^{3}$ , to $2 n^{2} /5 + O (n^{c})$ , for some $c < 2$ . We prove that the minimal n…

math.MG2019

On polyhedra inscribed in $S^{2}$ , with approximately equal edges

E. Makai

We consider triangle faced convex polyhedra inscribed in the unit sphere $S^{2}$ in $R^{3}$ . One way of measuring their deviation from regular polyhedra with triangular faces i…

math.MG2019

Inverse Blaschke-Santaló inequality for convex curves enclosing the origin several times

K. J. Böröczky, E. Makai

H. Guggenheimer generalized the planar volume product problem for locally convex curves $C$ enclosing the origin $k \geq 2$ times. He conjectured that the minimal volume product $V(…

math.MG2018

A colouring problem for the dodecahedral graph

Endre Makai, Tibor Tarnai

We consider vertex colourings of the dodecahedral graph with five colours, such that on each face the vertices are coloured with all the five colours. We show that the total number…

math.MG2018

Five-neighbour packings of centrally symmetric convex discs

Endre Makai

In an old paper of the author the thinnest five-neighbour packing of translates of a convex disc (different from a parallelogram) was determined. The minimal density was $3/7$ , and…