scholarly journals Discrete realizations of contact and intersection graphs (extended abstract)

1997 ◽  
pp. 359-370
Author(s):  
Jurek Czyzowicz ◽  
Evangelos Kranakis ◽  
Danny Krizanc ◽  
Jorge Urrutia
Keyword(s):  
Intersection Graphs

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.

scholarly journals Intersection Graphs of k-uniform Linear Hypergraphs

1982 ◽  
Vol 3 (2) ◽  
pp. 159-172 ◽  
Author(s):  
Ranjan N. Naik ◽  
S.B. Rao ◽  
S.S. Shrikhande ◽  
N.M. Singhi
Keyword(s):  
Intersection Graphs ◽  
Linear Hypergraphs

scholarly journals On the Isolated Vertices and Connectivity in Random Intersection Graphs

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Random Graphs ◽  
Intersection Graph ◽  
Intersection Graphs ◽  
Random Intersection Graph ◽  
Probability Of Connectivity ◽  
Asymptotic Probability

We study isolated vertices and connectivity in the random intersection graph . A Poisson convergence for the number of isolated vertices is determined at the threshold for absence of isolated vertices, which is equivalent to the threshold for connectivity. When and , we give the asymptotic probability of connectivity at the threshold for connectivity. Analogous results are well known in Erdős-Rényi random graphs.

scholarly journals Approximation Algorithms for Intersection Graphs

Algorithmica ◽  
2012 ◽  
Vol 68 (2) ◽  
pp. 312-336 ◽  
Author(s):  
Frank Kammer ◽  
Torsten Tholey
Keyword(s):  
Approximation Algorithms ◽  
Intersection Graphs

FUZZY INTERSECTION GRAPHS OF FUZZY SEMIGROUPS

2006 ◽  
Vol 02 (01) ◽  
pp. 1-10
Author(s):  
M. K. SEN ◽  
G. CHOWDHURY ◽  
D. S. MALIK
Keyword(s):  
Intersection Graph ◽  
Common Multiple ◽  
Intersection Graphs

Let S be a semigroup. This paper studies the intersection graphs of fuzzy semigroups. It is shown that the fuzzy intersection graph Int(G(S)), of S, is complete if and only if S is power joined. If Γ(S) denotes the set of all fuzzy right ideals of S, then the fuzzy intersection graph Int(Γ(S)) is complete if and only if S is fuzzy right uniform. Moreover, it is shown that Int(Γ(S)) is chordal if and only if for a,b,c,d ∈ S, some pair from {a,b,c,d} has a right common multiple property. It is also shown that if Int(G(S)) is complete and S has the acc on subsemigroups, then S is cyclic.

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