M. Cetina

activity

20082011

(\leq k)

-edges, 3-decomposable drawings, and the rectilinear crossing number of

K_{30}

12 citations · 15 across the 3 of their papers we have counts for

collaborators

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3 papers · 1 filter

math.CO2011★ 2 cited

On $(\leq k)$ -edges, crossings, and halving lines of geometric drawings of $K_{n}$

Bernardo M. Ábrego, Mario Cetina, Silvia Fernández-Merchant +2

Let $P$ be a set of points in general position in the plane. Join all pairs of points in $P$ with straight line segments. The number of segment-crossings in such a drawing, denoted…

math.CO2010★ 12 cited

Point sets that minimize $(\leq k)$ -edges, 3-decomposable drawings, and the rectilinear crossing number of $K_{30}$

M. Cetina, C. Hernández-Vélez, J. Leaños +1

There are two properties shared by all known crossing-minimizing geometric drawings of $K_{n}$ , for $n$ a multiple of 3. First, the underlying $n$ -point set of these drawings has exa…

math.CO2008★ 1 cited

3--symmetric and 3--decomposable drawings of $K_{n}$ (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 $K_{n}$ reveals two hard-to-miss features. First, all such drawings appear to be 3-fol…

On (≤k)-edges, crossings, and halving lines of geometric drawings of Kn​

Point sets that minimize (≤k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30​

3--symmetric and 3--decomposable drawings of Kn​ (extended version)

On $(\leq k)$ -edges, crossings, and halving lines of geometric drawings of $K_{n}$

Point sets that minimize $(\leq k)$ -edges, 3-decomposable drawings, and the rectilinear crossing number of $K_{30}$

3--symmetric and 3--decomposable drawings of $K_{n}$ (extended version)