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pro vyhledávání: '"ABREGO, BERNARDO"'
Autor:
Ábrego, Bernardo M., Fernández-Merchant, Silvia, Kano, Mikio, Orden, David, Pérez-Lantero, Pablo, Seara, Carlos, Tejel, Javier
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 21 no. 3 , Combinatorics (January 31, 2019) dmtcs:4537
We say that a finite set of red and blue points in the plane in general position can be $K_{1,3}$-covered if the set can be partitioned into subsets of size $4$, with $3$ points of one color and $1$ point of the other color, in such a way that, if at
Externí odkaz:
http://arxiv.org/abs/1707.06856
Autor:
Ábrego, Bernardo M., Dandurand, Julia, Fernández-Merchant, Silvia, Lagoda, Evgeniya, Sapozhnikov, Yakov
A $ k $-page book drawing of a graph $ G $ is a drawing of $ G $ on $ k $ halfplanes with common boundary $ l $, a line, where the vertices are on $ l $ and the edges cannot cross $ l $. The $ k $-page book crossing number of the graph $ G $, denoted
Externí odkaz:
http://arxiv.org/abs/1607.00131
Publikováno v:
In Procedia Computer Science 2021 195:275-279
Autor:
Ábrego, Bernardo M., Aichholzer, Oswin, Fernández-Merchant, Silvia, McQuillan, Dan, Mohar, Bojan, Mutzel, Petra, Ramos, Pedro, Richter, R. Bruce, Vogtenhuber, Birgit
The Harary--Hill conjecture, still open after more than 50 years, asserts that the crossing number of the complete graph $K_n$ is $ H(n) = \frac 1 4 \left\lfloor\frac{\mathstrut n}{\mathstrut 2}\right\rfloor \left\lfloor\frac{\mathstrut n-1}{\mathstr
Externí odkaz:
http://arxiv.org/abs/1510.00549
We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \}, $ \[ {\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3
Externí odkaz:
http://arxiv.org/abs/1508.07926
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 vertices all lie within an $n$-point subset of the plane is shown to be
Externí odkaz:
http://arxiv.org/abs/1501.00076
Akademický článek
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Akademický článek
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Autor:
Ábrego, Bernardo M., Aichholzer, Oswin, Fernández-Merchant, Silvia, Ramos, Pedro, Salazar, Gelasio
The Harary-Hill Conjecture States that the number of crossings in any drawing of the complete graph $ K_n $ in the plane is at least $Z(n):=\frac{1}{4}\left\lfloor \frac{n}{2}\right\rfloor \left\lfloor\frac{n-1}{2}\right\rfloor \left\lfloor \frac{n-2
Externí odkaz:
http://arxiv.org/abs/1309.3665
Autor:
Abrego, Bernardo M., Aichholzer, Oswin, Fernandez-Merchant, Silvia, Ramos, Pedro, Salazar, Gelasio
Around 1958, Hill described how to draw the complete graph $K_n$ with [Z(n) :=1/4\lfloor \frac{n}{2}\rfloor \lfloor \frac{n-1}{2}\rfloor \lfloor \frac{n-2}{2}% \rfloor \lfloor \frac{n-3}{2}\rfloor] crossings, and conjectured that the crossing number
Externí odkaz:
http://arxiv.org/abs/1206.5669