12 citations · 15 across the 3 of their papers we have counts for
4 papers
Visibility-preserving convexifications using single-vertex moves
Bernardo M. Abrego, Mario Cetina, Jesus Leanos +1
Devadoss asked: (1) can every polygon be convexified so that no internal visibility (between vertices) is lost in the process? Moreover, (2) does such a convexification exist, in w…
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…
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…
3--symmetric and 3--decomposable drawings of (extended version)
B. Ábrego, M. Cetina, S. Fernández--Merchant +2
Even the most superficial glance at the vast majority of crossing-minimal geometric drawings of reveals two hard-to-miss features. First, all such drawings appear to be 3-fol…