38 citations · 87 across the 11 of their papers we have counts for
12 papers
Bishellable drawings of
Bernardo M. Ábrego, Oswin Aichholzer, Silvia Fernández-Merchant +6
The Harary--Hill conjecture, still open after more than 50 years, asserts that the crossing number of the complete graph is $ H(n) = \frac 1 4 \left\lfloor\frac{\mathstrut n}…
Shellable drawings and the cylindrical crossing number of
Bernardo M. Ábrego, Oswin Aichholzer, Silvia Fernández-Merchant +2
The Harary-Hill Conjecture States that the number of crossings in any drawing of the complete graph in the plane is at least $Z(n):=\frac{1}{4}\left\lfloor \frac{n}{2}\righ…
Empty triangles in good drawings of the complete graph
Oswin Aichholzer, Thomas Hackl, Alexander Pilz +3
A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting…
The 2-page crossing number of
Bernardo M. Abrego, Oswin Aichholzer, Silvia Fernandez-Merchant +2
Around 1958, Hill described how to draw the complete graph with [Z(n) :=1/4\lfloor \frac{n}{2}\rfloor \lfloor \frac{n-1}{2}\rfloor \lfloor \frac{n-2}{2}% \rfloor \lfloor \fra…
On k-Convex Polygons
Oswin Aichholzer, Franz Aurenhammer, Erik D. Demaine +3
We introduce a notion of -convexity and explore polygons in the plane that have this property. Polygons which are \mbox{-convex} can be triangulated with fast yet simple algo…
Balanced lines in two-coloured point sets
David Orden, Pedro Ramos, Gelasio Salazar
Let and be point sets (of {\em blue} and {\em red} points, respectively) in the plane, such that is in general position, and is even. A line is {\…