12 citations · 23 across the 4 of their papers we have counts for
8 papers
Counting the Number of Crossings in Geometric Graphs
Frank Duque, Ruy Fabila-Monroy, César Hernández-Vélez +1
A geometric graph is a graph whose vertices are points in general position in the plane and its edges are straight line segments joining these points. In this paper we give an $O(n…
The complexity of computing the cylindrical and the -circle crossing number of a graph
Frank Duque, Hernán González-Aguilar, César Hernández-Vélez +2
A plane drawing of a graph is {\em cylindrical} if there exist two concentric circles that contain all the vertices of the graph, and no edge intersects (other than at its endpoint…
Spanning trees with nonseparating paths
Cristina G. Fernandes, César Hernández-Vélez, Orlando Lee +1
We consider questions related to the existence of spanning trees in graphs with the property that after the removal of any path in the tree the graph remains connected. We show tha…
On the pseudolinear crossing number
Cesar Hernandez-Velez, Jesus Leanos, Gelasio Salazar
A drawing of a graph is {\em pseudolinear} if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The {\em pseudolinear crossing n…
The optimal drawings of K_{5,n}
Cesar Hernandez-Velez, Carolina Medina, Gelasio Salazar
Zarankiewicz's Conjecture (ZC) states that the crossing number cr equals $Z(m,n):=\floor{\frac{m}{2}} \floor{\frac{m-1}{2}} \floor{\frac{n}{2}} \floor{\frac{n-1}{2}}$. S…
Making a graph crossing-critical by multiplying its edges
Laurent Beaudou, César Hernández-Vélez, Gelasio Salazar
A graph is crossing-critical if the removal of any of its edges decreases its crossing number. This work is motivated by the following question: to what extent is crossing- critica…
Point sets that minimize -edges, 3-decomposable drawings, and the rectilinear crossing number of
M. Cetina, C. Hernández-Vélez, J. Leaños +1
There are two properties shared by all known crossing-minimizing geometric drawings of , for a multiple of 3. First, the underlying -point set of these drawings has exa…
Nested cycles in large triangulations and crossing-critical graphs
Cesar Hernandez-Velez, Gelasio Salazar, Robin Thomas
We show that every sufficiently large plane triangulation has a large collection of nested cycles that either are pairwise disjoint, or pairwise intersect in exactly one vertex, or…