30 citations · 65 across the 19 of their papers we have counts for
5 papers · 1 filter
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…