R. Fulek

activity

20092020

most citedCrossing numbers and combinatorial characterization of monotone drawings of

K_{n}

30 citations · 65 across the 19 of their papers we have counts for

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13 papers · 1 filter

cs.CG2020

Polygons with Prescribed Angles in 2D and 3D

Alon Efrat, Radoslav Fulek, Stephen Kobourov +1

We consider the construction of a polygon $P$ with $n$ vertices whose turning angles at the vertices are given by a sequence $A = (α_{0}, \dots, α_{n - 1})$ , $α_{i} \in (- π, π)$ , for $i\in\{…

cs.CG2019

Atomic Embeddability, Clustered Planarity, and Thickenability

Radoslav Fulek, Csaba D. Tóth

We study the atomic embeddability testing problem, which is a common generalization of clustered planarity (c-planarity, for short) and thickenability testing, and present a polyno…

cs.CG2018

The Crossing Tverberg Theorem

Radoslav Fulek, Bernd Gärtner, Andrey Kupavskii +2

Tverberg's theorem is one of the cornerstones of discrete geometry. It states that, given a set $X$ of at least $(d + 1) (r - 1) + 1$ points in $R^{d}$ , one can find a partition $X=…

cs.CG2018

Crossing Minimization in Perturbed Drawings

Radoslav Fulek, Csaba D. Tóth

Due to data compression or low resolution, nearby vertices and edges of a graph drawing may be bundled to a common node or arc. We model such a `compromised' drawing by a piecewise…

cs.CG2017

Recognizing Weak Embeddings of Graphs

Hugo A. Akitaya, Radoslav Fulek, Csaba D. Tóth

We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding $φ : G \to M$ of a graph $G$ into a 2-manifold $M$ maps…

cs.CG2017

Hanani-Tutte for approximating maps of graphs

Radoslav Fulek, Jan Kynčl

We resolve in the affirmative conjectures of Repovs and A. Skopenkov (1998), and M. Skopenkov (2003) generalizing the classical Hanani-Tutte theorem to the setting of approximating…

cs.CG2016

Bounded embeddings of graphs in the plane

Radoslav Fulek

A drawing in the plane ( $R^{2}$ ) of a graph $G = (V, E)$ equipped with a function $γ : V \to N$ is \emph{ $x$ -bounded} if (i) $x (u) < x (v)$ whenever $γ (u) < γ (v)$ a…

cs.CG2016

Hanani-Tutte for Radial Planarity II

Radoslav Fulek, Michael Pelsmajer, Marcus Schaefer

A drawing of a graph $G$ is radial if the vertices of $G$ are placed on concentric circles $C_{1}, \dots, C_{k}$ with common center $c$ , and edges are drawn radially: every edge inter…

cs.CG2016

Embedding graphs into embedded graphs

Radoslav Fulek

A (possibly denerate) drawing of a graph $G$ in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that t…

cs.CG2016

C-planarity of Embedded Cyclic c-Graphs

Radoslav Fulek

We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler gra…

cs.CG2014★ 4 cited

Toward the Hanani-Tutte Theorem for Clustered Graphs

Radoslav Fulek

The weak variant of Hanani-Tutte theorem says that a graph is planar, if it can be drawn in the plane so that every pair of edges cross an even number of times. Moreover, we can tu…

cs.CG2013

Clustered planarity testing revisited

Radoslav Fulek, Jan Kynčl, Igor Malinović +1

The Hanani--Tutte theorem is a classical result proved for the first time in the 1930s that characterizes planar graphs as graphs that admit a drawing in the plane in which every p…

cs.CG2012★ 6 cited

Universal point sets for planar three-tree

Radoslav Fulek, Csaba D. Tóth

For every $n \in N$ , we present a set $S_{n}$ of $O (n^{3/2} lo g n)$ points in the plane such that every planar 3-tree with $n$ vertices has a straight-line embedding in the p…