Let S be a set of points in the plane. What is the minimum possible dilation of all plane graphs that contain S? Even for a set S as simple as five points evenly placed on the ci...
Pinchasi and Radoiˇci´c [11] used the following observation to bound the number of edges of a topological graph without a self-crossing cycle of length 4: if we make a list of t...
We show that the vertices of any plane graph in which every face is of length at least g can be colored by (3g - 5)/4 colors so that every color appears in every face. This is nea...
Noga Alon, Robert Berke, Kevin Buchin, Maike Buchi...
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is th...
Embedding metrics into constant-dimensional geometric spaces, such as the Euclidean plane, is relatively poorly understood. Motivated by applications in visualization, ad-hoc netw...
MohammadHossein Bateni, Mohammad Taghi Hajiaghayi,...