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pro vyhledávání: '"Ackerman, Eyal"'
A long-standing open conjecture of Branko Gr\"unbaum from 1972 states that any simple arrangement of $n$ pairwise intersecting pseudocircles in the plane can have at most $2n-2$ digons. Agarwal et al. proved this conjecture for arrangements of pairwi
Externí odkaz:
http://arxiv.org/abs/2406.02276
Autor:
Ackerman, Eyal, Keszegh, Balázs
An adjacency-crossing graph is a graph that can be drawn such that every two edges that cross the same edge share a common endpoint. We show that the number of edges in an $n$-vertex adjacency-crossing graph is at most $5n-10$. If we require the edge
Externí odkaz:
http://arxiv.org/abs/2309.06507
Autor:
Ackerman, Eyal, Keszegh, Balázs
Let $\cal C$ be a set of curves in the plane such that no three curves in $\cal C$ intersect at a single point and every pair of curves in $\cal C$ intersect at exactly one point which is either a crossing or a touching point. According to a conjectu
Externí odkaz:
http://arxiv.org/abs/2305.13807
Publikováno v:
In European Journal of Combinatorics October 2024 121
Autor:
Ackerman, Eyal, Keszegh, Balázs
Publikováno v:
In European Journal of Combinatorics May 2024 118
We prove that there are $O(n)$ tangencies among any set of $n$ red and blue planar curves in which every pair of curves intersects at most once and no two curves of the same color intersect. If every pair of curves may intersect more than once, then
Externí odkaz:
http://arxiv.org/abs/2103.02960
Publikováno v:
Discrete and Computational Geometry 68 (2022), 1049-1077
What is the maximum number of intersections of the boundaries of a simple $m$-gon and a simple $n$-gon, assuming general position? This is a basic question in combinatorial geometry, and the answer is easy if at least one of $m$ and $n$ is even: If b
Externí odkaz:
http://arxiv.org/abs/2002.05680
What is the minimum number of colors that always suffice to color every planar set of points such that any disk that contains enough points contains two points of different colors? It is known that the answer to this question is either three or four.
Externí odkaz:
http://arxiv.org/abs/1902.08468
Autor:
Ackerman, Eyal, Pinchasi, Rom
Let $A$ and $B$ be finite sets and consider a partition of the \emph{discrete box} $A \times B$ into \emph{sub-boxes} of the form $A' \times B'$ where $A' \subset A$ and $B' \subset B$. We say that such a partition has the $(k,\ell)$-piercing propert
Externí odkaz:
http://arxiv.org/abs/1812.08396
We consider geometric hypergraphs whose vertex set is a finite set of points (e.g., in the plane), and whose hyperedges are the intersections of this set with a family of geometric regions (e.g., axis-parallel rectangles). A typical coloring problem
Externí odkaz:
http://arxiv.org/abs/1806.03931