6 citations · 18 across the 7 of their papers we have counts for
8 papers
The balanced upper chromatic number of linear hypergraphs and the -cube over elements
Gabriela Araujo-Pardo, Silvia Fernández-Merchant, Adriana Hansberg +3
A coloring of the vertices of a hypergraph is called \emph{balanced} if the sizes of the color classes differ by at most one. We say that a hyperedge is \emph{rainbow} if its eleme…
-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…
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…
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 -edges, crossings, and halving lines of geometric drawings of
Bernardo M. Ábrego, Mario Cetina, Silvia Fernández-Merchant +2
Let be a set of points in general position in the plane. Join all pairs of points in with straight line segments. The number of segment-crossings in such a drawing, denoted…
On 3-decomposable geometric drawings of
Bernardo Abrego, Silvia Fernandez-Merchant, Jesus Leanos +1
The point sets of all known optimal rectilinear drawings of share an unmistakeable clustering property, the so--called {\em 3--decomposability}. It is widely believed that th…