30 citations · 65 across the 19 of their papers we have counts for
16 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…
Diameter Bounds for Planar Graphs
Radoslav Fulek, Filip Morić, David Pritchard
The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inver…
On disjoint crossing families in geometric graphs
Radoslav Fulek, Andrew Suk
A geometric graph is a graph drawn in the plane with vertices represented by points and edges as straight-line segments. A geometric graph contains a (k,l)-crossing family if there…
A computational approach to Conway's thrackle conjecture
Radoslav Fulek, Janos Pach
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum n…
Drawing Graphs with Orthogonal Crossings
Radoslav Fulek, Balázs Keszegh, Filip Morić
By a poly-line drawing of a graph G on n vertices we understand a drawing of G in the plane such that each edge is represented by a polygonal arc joining its two respective vertice…
Coloring geometric hyper-graph defined by an arrangement of half-planes
Radoslav Fulek
We prove that any finite set of half-planes can be colored by two colors so that every point of the plane, which belongs to at least three half-planes in the set, is covered by hal…
On Polygons Excluding Point Sets
Radoslav Fulek, Balázs Keszegh, Filip Morić +1
By a polygonization of a finite point set in the plane we understand a simple polygon having as the set of its vertices. Let and be sets of blue and red points, res…