6 papers · 1 filter
Three-chromatic geometric hypergraphs
Gábor Damásdi, Dömötör Pálvölgyi
We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no trans…
Crumby colorings -- red-blue vertex partition of subcubic graphs regarding a conjecture of Thomassen
János Barát, Zoltán L. Blázsik, Gábor Damásdi
Thomassen formulated the following conjecture: Every -connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree at most (that is, i…
Odd wheels are not odd-distance graphs
Gábor Damásdi
An odd wheel graph is a graph formed by connecting a new vertex to all vertices of an odd cycle. We answer a question of Rosenfeld and Le by showing that odd wheels cannot be drawn…
Saturation problems in the Ramsey theory of graphs, posets and point sets
Gábor Damásdi, Balázs Keszegh, David Malec +3
In 1964, Erdős, Hajnal and Moon introduced a saturation version of Turán's classical theorem in extremal graph theory. In particular, they determined the minimum number of edges in…
On Covering Numbers, Young Diagrams, and the Local Dimension of Posets
Gábor Damásdi, Stefan Felsner, António Girão +4
We study covering numbers and local covering numbers with respect to difference graphs and complete bipartite graphs. In particular we show that in every cover of a Young diagram w…
Triangle areas in line arrangements
Gábor Damásdi, Leonardo Martínez-Sandoval, Dániel T. Nagy +1
A widely investigated subject in combinatorial geometry, originated from Erdős, is the following. Given a point set of cardinality in the plane, how can we describe the dis…