Extremal problems for geometric hypergraphs

1996 ◽  
pp. 105-114 ◽  
Author(s):  
Tamal K. Dey ◽  
János Pach
Keyword(s):  
Extremal Problems ◽  
Geometric Hypergraphs

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.

scholarly journals Extremal Problems for Geometric Hypergraphs

1998 ◽  
Vol 19 (4) ◽  
pp. 473-484 ◽  
Author(s):  
T. K. Dey ◽  
J. Pach
Keyword(s):  
Extremal Problems ◽  
Geometric Hypergraphs

Some extremal problems for circular polygons

1996 ◽  
Vol 80 (4) ◽  
pp. 1956-1961
Author(s):  
A. Yu. Solynin
Keyword(s):  
Extremal Problems

Some extremal problems on classes of summable functions

1972 ◽  
Vol 24 (5) ◽  
pp. 574-578
Author(s):  
L. G. Khomutenko
Keyword(s):  
Extremal Problems
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