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Descripción
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| In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: \begin{enumerate} \item We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq k)$-edges for a fixed $k\leq \lfloor n/3 \rfloor -1$; \item We show that the new lower bound $3\binom{k+2}{2}+3\binom{k-\lfloor \frac{n}{3} \rfloor+2}{2}$ for the number of $(\leq k)$-edges of a planar point set shown in \cite{AGOR-06} is optimal in the range $\lfloor n/3 \rfloor \leq k \leq \lfloor 5n/12 \rfloor -1$; \item We show that for $k < n/4$ the number of $(\leq k)$-facets of a set of $n$ points in~$\mathbb{R}^3$ in general position is at least $4\binom{k+3}{3}$, and that this bound is tight in that range. \end{enumerate} | |
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Internacional
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Si |
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Nombre congreso
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European Conference on Combinatorics, Graph Theory and Applications |
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Tipo de participación
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960 |
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Lugar del congreso
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Sevilla, España |
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Revisores
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Si |
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ISBN o ISSN
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1571-0653 |
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DOI
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Fecha inicio congreso
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11/09/2007 |
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Fecha fin congreso
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15/09/2007 |
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