73 citations · 178 across the 49 of their papers we have counts for
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Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem
Jonathan Klawitter, Martin Nöllenburg, Torsten Ueckerdt
We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies o…
Splitting Planar Graphs of Girth 6 into Two Linear Forests with Short Paths
Maria Axenovich, Torsten Ueckerdt, Pascal Weiner
Recently, Borodin, Kostochka, and Yancey (On -improper -coloring of sparse graphs. Discrete Mathematics, 313(22), 2013) showed that the vertices of each planar graph of girth…
Pixel and Voxel Representations of Graphs
Muhammad Jawaherul Alam, Thomas Bläsius, Ignaz Rutter +2
We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose…
Conditions on Ramsey non-equivalence
Maria Axenovich, Jonathan Rollin, Torsten Ueckerdt
Given a graph H, a graph G is called a Ramsey graph of H if there is a monochromatic copy of H in every coloring of the edges of G with two colors. Two graphs G, H are called Ramse…
Phase locking a clock oscillator to a coherent atomic ensemble
R. Kohlhaas, A. Bertoldi, E. Cantin +3
The sensitivity of an atomic interferometer increases when the phase evolution of its quantum superposition state is measured over a longer interrogation interval. In practice, a l…
Contact Representations of Sparse Planar Graphs
Md. Jawaherul Alam, David Eppstein, Michael Kaufmann +4
We study representations of graphs by contacts of circular arcs, CCA-representations for short, where the vertices are interior-disjoint circular arcs in the plane and each edge is…