11 papers
Covering a square by congruent squares
György Dósa, Zsolt Lángi, Zsolt Tuza
The main goal of this paper is to address the following problem: given a positive integer , find the largest value such that a square of edge length in the Euclide…
Notes on non-separable arrangements of convex bodies
Károly Bezdek, Zsolt Lángi
A problem posed by ErdÅs in 1945 initiated the study of non-separable arrangements of convex bodies. A finite collection of convex bodies in Euclidean -space is called a non-se…
The Honeycomb Conjecture in normed planes and an alpha-convex variant of a theorem of Dowker
Zsolt Lángi, Shanshan Wang
The Honeycomb Conjecture states that among tilings with unit area cells in the Euclidean plane, the average perimeter of a cell is minimal for a regular hexagonal tiling. This conj…
On the edge densities of normal, convex mosaics
Máté Kadlicskó, Zsolt Lángi, Shanxiang Lyu
In this paper we investigate the problem of finding the minimum edge density in families of convex, normal mosaics with unit volume cells in -dimensional Euclidean space. In the…
Curves with increasing chords in normed planes
Zsolt Lángi, Sára Lengyel
A curve has the increasing chord property if for any points in this order on the curve, the distance of is not smaller than that of . Answering a conjecture of…
Arcs with increasing chords in
Adrian Dumitrescu, Zsolt Lángi
A curve that connects and has the increasing chord property if whenever lie in that order on . For planar curves, the length of such a c…