28 citations · 48 across the 11 of their papers we have counts for
15 papers
-covering red and blue points in the plane
Bernardo M. Ábrego, Silvia Fernández-Merchant, Mikio Kano +4
We say that a finite set of red and blue points in the plane in general position can be -covered if the set can be partitioned into subsets of size , with points of…
Book crossing numbers of the complete graph and small local convex crossing numbers
Bernardo M. Ábrego, Julia Dandurand, Silvia Fernández-Merchant +2
A -page book drawing of a graph is a drawing of on halfplanes with common boundary , a line, where the vertices are on and the edges cannot cross…
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}…
The rectilinear local crossing number of
Bernardo M. Ábrego, Silvia Fernández-Merchant
We determine , the rectilinear local crossing number of the complete graph for every . More precisely, for every \[ {\bar{\r…
On The Number of Similar Instances of a Pattern in a Finite Set
Bernardo Abrego, Silvia Fernandez-Merchant, Daniel J. Katz +1
New bounds on the number of similar or directly similar copies of a pattern within a finite subset of the line or the plane are proved. The number of equilateral triangles whose ve…
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…