30 citations · 65 across the 19 of their papers we have counts for
33 papers
Saturation problems about forbidden - submatrices
Radoslav Fulek, Balázs Keszegh
A - matrix is saturating for a - matrix if does not contain a submatrix that can be turned into by changing some entries to entries, and changin…
Strong Hanani-Tutte for the Torus
Radoslav Fulek, Michael J. Pelsmajer, Marcus Schaefer
If a graph can be drawn on the torus so that every two independent edges cross an even number of times, then the graph can be embedded on the torus.
Polygons with Prescribed Angles in 2D and 3D
Alon Efrat, Radoslav Fulek, Stephen Kobourov +1
We consider the construction of a polygon with vertices whose turning angles at the vertices are given by a sequence , , for $i\in\{…
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…
Z_2-genus of graphs and minimum rank of partial symmetric matrices
Radoslav Fulek, Jan Kynčl
The \emph{genus} of a graph is the minimum such that has an embedding on the orientable surface of genus . A drawing of a graph on a surface is…
A Note on a Picture-Hanging Puzzle
Radoslav Fulek, Sergey Avvakumov
In the picture-hanging puzzle we are to hang a picture so that the string loops around nails and the removal of any nail results in a fall of the picture. We show that the leng…
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 of at least points in , one can find a partition $X=…
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…
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 of a graph into a 2-manifold maps…
Counterexample to an extension of the Hanani-Tutte theorem on the surface of genus 4
Radoslav Fulek, Jan Kynčl
We find a graph of genus and its drawing on the orientable surface of genus with every pair of independent edges crossing an even number of times. This shows that the stron…
Thrackles: An Improved Upper Bound
Radoslav Fulek, János Pach
A {\em thrackle} is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle…
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…
On the Existence of Ordinary Triangles
Radoslav Fulek, Hossein Nassajian Mojarrad, Márton Naszódi +3
Let be a finite point set in the plane. A \emph{-ordinary triangle} in is a subset of consisting of three non-collinear points such that each of the three lines dete…
Unified Hanani-Tutte theorem
Radoslav Fulek, Jan Kynčl, Dömötör Pálvölgyi
We introduce a common generalization of the strong Hanani-Tutte theorem and the weak Hanani-Tutte theorem: if a graph has a drawing in the plane where every pair of indepen…
Bounded embeddings of graphs in the plane
Radoslav Fulek
A drawing in the plane () of a graph equipped with a function is \emph{-bounded} if (i) whenever a…
Hanani-Tutte for Radial Planarity II
Radoslav Fulek, Michael Pelsmajer, Marcus Schaefer
A drawing of a graph is radial if the vertices of are placed on concentric circles with common center , and edges are drawn radially: every edge inter…
Embedding graphs into embedded graphs
Radoslav Fulek
A (possibly denerate) drawing of a graph 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…
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…
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…
Crossing numbers and combinatorial characterization of monotone drawings of
Martin Balko, Radoslav Fulek, Jan Kynčl
In 1958, Hill conjectured that the minimum number of crossings in a drawing of is exactly $Z(n) = \frac{1}{4} \lfloor\frac{n}{2}\rfloor \left\lfloor\frac{n-1}{2}\right\rfloor…
Extending Partial Representations of Circle Graphs
Steven Chaplick, Radoslav Fulek, Pavel Klavík
The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We s…
Estimating the number of disjoint edges in simple topological graphs via cylindrical drawings
Radoslav Fulek
A topological graph drawn on a cylinder whose base is horizontal is \emph{angularly monotone} if every vertical line intersects every edge at most once. Let denote the maxim…
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…
Homometric sets in trees
Radoslav Fulek, Slobodan Mitrović
Let denote a simple graph with the vertex set and the edge set . The profile of a vertex set denotes the multiset of pairwise distances between t…