scholarly journals Integer Representations of Convex Polygon Intersection Graphs

2013 ◽  
Vol 27 (1) ◽  
pp. 205-231 ◽  
Author(s):  
Tobias Müller ◽  
Erik Jan van Leeuwen ◽  
Jan van Leeuwen
Keyword(s):  
Convex Polygon ◽  
Intersection Graphs ◽  
Polygon Intersection

scholarly journals Turán-type results for intersection graphs of boxes

2021 ◽  
pp. 1-6
Author(s):  
István Tomon ◽  
Dmitriy Zakharov
Keyword(s):  
Short Note ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Poset Dimension ◽  
Axis Parallel ◽  
Turán Theorem ◽  
Separation Dimension

Abstract In this short note, we prove the following analog of the Kővári–Sós–Turán theorem for intersection graphs of boxes. If G is the intersection graph of n axis-parallel boxes in $${{\mathbb{R}}^d}$$ such that G contains no copy of K t,t , then G has at most ctn( log n)2d+3 edges, where c = c(d)>0 only depends on d. Our proof is based on exploring connections between boxicity, separation dimension and poset dimension. Using this approach, we also show that a construction of Basit, Chernikov, Starchenko, Tao and Tran of K2,2-free incidence graphs of points and rectangles in the plane can be used to disprove a conjecture of Alon, Basavaraju, Chandran, Mathew and Rajendraprasad. We show that there exist graphs of separation dimension 4 having superlinear number of edges.

Learning gradual rules to model convex polygon-shaped classes

2010 ◽  
Author(s):  
Lavinia Darlea ◽  
Sylvie Galichet ◽  
Lionel Valet ◽  
Gabriel Vasile ◽  
Emmanuel Trouve
Keyword(s):  
Convex Polygon
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