Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Perles, Micha A."'
Autor:
Keller, Chaya, Perles, Micha A.
A family $\mathcal{F}$ of sets satisfies the $(p,q)$-property if among every $p$ members of $\mathcal{F}$, some $q$ can be pierced by a single point. The celebrated $(p,q)$-theorem of Alon and Kleitman asserts that for any $p \geq q \geq d+1$, any fa
Externí odkaz:
http://arxiv.org/abs/2306.02181
Autor:
Keller, Chaya, Perles, Micha A.
For a family $\mathcal{F}$ of sets in $\mathbb{R}^d$, the Krasnoselskii number of $\mathcal{F}$ is the smallest $m$ such that for any $S \in \mathcal{F}$, if every $m$ points of $S$ are visible from a common point in $S$, then any finite subset of $S
Externí odkaz:
http://arxiv.org/abs/2012.06014
Autor:
Keller, Chaya, Perles, Micha A.
Let G be a complete convex geometric graph, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that has an edge in common with every element of F. In [C. Keller and M. A. Perles, Blockers for simple
Externí odkaz:
http://arxiv.org/abs/1806.02178
Autor:
Keller, Chaya, Perles, Micha A.
Let G be a complete convex geometric graph on 2m vertices, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that meets every element of F. In [C. Keller and M. A. Perles, On the smallest sets bloc
Externí odkaz:
http://arxiv.org/abs/1607.01034
Autor:
Keller, Chaya, Perles, Micha A.
Let P be a finite set of points in general position in the plane. The structure of the complete graph K(P) as a geometric graph includes, for any pair [a,b],[c,d] of vertex-disjoint edges, the information whether they cross or not. The simple (i.e.,
Externí odkaz:
http://arxiv.org/abs/1412.8400
Autor:
Perles, Micha A., Sigron, Moriah
We say that a finite set S of points in R^d is in "strong general position" if for any collection {F_1,..., F_r} of r pairwise disjoint subsets of S (1 <= r <= |S|) we have: d-dim (the intersection of aff F_1,aff F_2,...,aff F_r) = min{d+1, (d-dim af
Externí odkaz:
http://arxiv.org/abs/1409.2899
Autor:
Keller, Chaya, Perles, Micha A.
A well-known result of Kupitz from 1982 asserts that the maximal number of edges in a convex geometric graph (CGG) on $n$ vertices that does not contain $k+1$ pairwise disjoint edges is $kn$ (provided $n>2k$). For $k=1$ and $k=n/2-1$, the extremal ex
Externí odkaz:
http://arxiv.org/abs/1405.4019
In this paper we present a complete characterization of the smallest sets that block all the simple spanning trees (SSTs) in a complete geometric graph. We also show that if a subgraph is a blocker for all SSTs of diameter at most 4, then it must blo
Externí odkaz:
http://arxiv.org/abs/1201.4782
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple $n$-gon, $n \ge 3$, in the plane as a function of $n$, and describe an $n$-gon $(n \ge 3)$ for which both upper bounds (for the interior and the exteri
Externí odkaz:
http://arxiv.org/abs/1012.3541
Autor:
Keller, Chaya, Perles, Micha A.
Consider the complete convex geometric graph on $2m$ vertices, $CGG(2m)$, i.e., the set of all boundary edges and diagonals of a planar convex $2m$-gon $P$. In [C. Keller and M. Perles, On the Smallest Sets Blocking Simple Perfect Matchings in a Conv
Externí odkaz:
http://arxiv.org/abs/1011.5883