Some extremal problems in combinatorial geometry

1978 ◽  
pp. 308-312 ◽  
Author(s):  
E. G. Straus
Keyword(s):  
Combinatorial Geometry ◽  
Extremal Problems

scholarly journals Extremal problems for convex geometric hypergraphs and ordered hypergraphs

2020 ◽  
pp. 1-19
Author(s):  
Zoltán Füredi ◽  
Tao Jiang ◽  
Alexandr Kostochka ◽  
Dhruv Mubayi ◽  
Jacques Verstraëte
Keyword(s):  
Extremal Function ◽  
Combinatorial Geometry ◽  
Extremal Problems ◽  
Geometric Graphs ◽  
Uniform Hypergraphs ◽  
Vertex Set ◽  
Order Of Magnitude ◽  
The Extremal Function ◽  
Geometric Hypergraphs ◽  
Rich History

Abstract An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich history with applications to a variety of problems in combinatorial geometry. In this paper, we consider analogous extremal problems for uniform hypergraphs, and determine the order of magnitude of the extremal function for various ordered and convex geometric paths and matchings. Our results generalize earlier works of Braı–Károlyi–Valtr, Capoyleas–Pach, and Aronov–Dujmovič–Morin–Ooms-da Silveira. We also provide a new variation of the Erdős-Ko-Rado theorem in the ordered setting.

Results and Problems in Combinatorial Geometry

1985 ◽  
Author(s):  
Vladimir G. Boltjansky ◽  
Israel Gohberg
Keyword(s):  
Combinatorial Geometry

scholarly journals Quantitative combinatorial geometry for concave functions

2021 ◽  
Vol 182 ◽  
pp. 105465
Author(s):  
Sherry Sarkar ◽  
Alexander Xue ◽  
Pablo Soberón
Keyword(s):  
Combinatorial Geometry ◽  
Concave Functions
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