A superlinear lower bound on the number of 5-holes
From MaRDI portal
Publication:2306008
DOI10.1016/j.jcta.2020.105236zbMath1432.52028OpenAlexW2596764499WikidataQ112881842 ScholiaQ112881842MaRDI QIDQ2306008
Jan Kynčl, Martin Balko, Manfred Scheucher, Irene Parada, Birgit Vogtenhuber, Thomas Hackl, Oswin Aichholzer, Pavel Valtr
Publication date: 20 March 2020
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://drops.dagstuhl.de/opus/volltexte/2017/7200/
Erd?s problems and related topics of discrete geometry (52C10) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05) Combinatorial complexity of geometric structures (52C45) Computer assisted proofs of proofs-by-exhaustion type (68V05)
Related Items
On convex holes in d-dimensional point sets, On weighted sums of numbers of convex polygons in point sets, Holes and islands in random point sets, Tight bounds on the expected number of holes in random point sets, Empty Triangles in Generalized Twisted Drawings of $K_n$
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Generalized ham-sandwich cuts
- Abstract order type extension and new results on the rectilinear crossing number
- Convex independent sets and 7-holes in restricted planar point sets
- Sets in \(\mathbb{R}^ d\) with no large empty convex subsets
- Konvexe Fünfecke in ebenen Punktmengen
- Enumerating order types for small point sets with applications
- Finding sets of points without empty convex 6-gons
- Crossing numbers and combinatorial characterization of monotone drawings of \(K_n\)
- On empty convex polygons in a planar point set
- Lower bounds for the number of small convex \(k\)-holes
- The empty hexagon theorem
- Empty convex hexagons in planar point sets
- Multidimensional Sorting
- Research Problems in Discrete Geometry
- Sets with No Empty Convex 7-Gons
- Empty Simplices in Euclidean Space
- A superlinear lower bound on the number of 5-holes
- On 5-Gons and 5-Holes
- A Note on the Number of Empty Triangles
- Planar point sets with a small number of empty convex polygons
- Sweeps, arrangements and signotopes
