6 citations · 8 across the 7 of their papers we have counts for
9 papers
Extending Bilipschitz Mappings between Separated Nets
Michael Dymond, Vojtěch Kaluža
We provide a new characterisation of the decades old open problem of extending bilipschitz mappings given on a Euclidean separated net. In particular, this allows for the complete…
Three observations on the Colin de Verdière spectral graph parameter
Vojtěch Kaluža, Vadym Koval
In this small note, we collect several observations pertaining to the famous spectral graph parameter introduced in 1990 by Y. Colin de Verdière. This parameter is defined as t…
Planar Bilipschitz Extension from Separated Nets
Michael Dymond, Vojtěch Kaluža
We prove that every -bilipschitz mapping can be extended to a -bilipschitz mapping and provide a polynomial upp…
Divergence of separated nets with respect to displacement equivalence
Michael Dymond, Vojtěch Kaluža
We introduce a hierachy of equivalence relations on the set of separated nets of a given Euclidean space, indexed by concave increasing functions .…
Even maps, the Colin de~Verdière number and representations of graphs
Vojtěch Kaluža, Martin Tancer
Van der Holst and Pendavingh introduced a graph parameter , which coincides with the more famous Colin de Verdière graph parameter for small values. However, the definition…
Highly irregular separated nets
Michael Dymond, Vojtěch Kaluža
In 1998 Burago and Kleiner and (independently) McMullen gave examples of separated nets in Euclidean space which are non-bilipschitz equivalent to the integer lattice. We study wea…
Mapping grid points onto a square forces an arbitrarily large Lipschitz constant
Michael Dymond, Vojtěch Kaluža, Eva Kopecká
We prove that the regular square grid of points in the integer lattice cannot be recovered from an arbitrary -element subset of …
A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane
Éric Colin de Verdière, Vojtěch Kaluža, Pavel Paták +2
We reprove the strong Hanani-Tutte theorem on the projective plane. In contrast to the previous proof by Pelsmajer, Schaefer and Stasi, our method is constructive and does not rely…
Shortest path embeddings of graphs on surfaces
Alfredo Hubard, Vojtěch Kaluža, Arnaud de Mesmay +1
The classical theorem of Fáry states that every planar graph can be represented by an embedding in which every edge is represented by a straight line segment. We consider generaliz…