8 citations · 21 across the 8 of their papers we have counts for
8 papers
Drawing cubic graphs with the four basic slopes
Padmini Mukkamala, Dömötör Pálvölgyi
We show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes . We also prove that four slopes have this pr…
Saturating Sperner families
Dániel Gerbner, Balázs Keszegh, Nathan Lemons +3
A family $\cF \subseteq 2^{[n]}$ saturates the monotone decreasing property $\cP$ if $\cF$ satisfies $\cP$ and one cannot add any set to $\cF$ such that property $\cP$ is still sat…
Lower bounds on the obstacle number of graphs
Padmini Mukkamala, János Pach, Dömötör Pálvölgyi
Given a graph , an {\em obstacle representation} of is a set of points in the plane representing the vertices of , together with a set of connected obstacles such that tw…
Decomposition of Geometric Set Systems and Graphs
Dömötör Pálvölgyi
We study two decomposition problems in combinatorial geometry. The first part deals with the decomposition of multiple coverings of the plane. We say that a planar set is cover-dec…
Drawing planar graphs of bounded degree with few slopes
Balázs Keszegh, János Pach, Dömötör Pálvölgyi
We settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists a function with the property that every planar graph with maximum degree admi…
Consistent digital line segments
Tobias Christ, Dömötör Pálvölgyi, Miloš Stojaković
We introduce a novel and general approach for digitalization of line segments in the plane that satisfies a set of axioms naturally arising from Euclidean axioms. In particular, we…