scholarly journals Graph Products Revisited: Tight Approximation Hardness of Induced Matching, Poset Dimension and More

2013 ◽  
Author(s):  
Parinya Chalermsook ◽  
Bundit Laekhanukit ◽  
Danupon Nanongkai
Keyword(s):  
Graph Products ◽  
Induced Matching ◽  
Approximation Hardness ◽  
Poset Dimension

scholarly journals Inapproximability of Rank, Clique, Boolean, and Maximum Induced Matching-Widths under Small Set Expansion Hypothesis

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 173 ◽  
Author(s):  
Koichi Yamazaki
Keyword(s):  
Approximation Algorithm ◽  
Induced Matching ◽  
Time Approximation ◽  
Approximation Factor ◽  
Approximation Hardness ◽  
Polynomial Time Approximation Algorithm ◽  
Small Set ◽  
Tree Width ◽  
Similar Approximation ◽  
Maximum Induced Matching

Wu et al. (2014) showed that under the small set expansion hypothesis (SSEH) there is no polynomial time approximation algorithm with any constant approximation factor for several graph width parameters, including tree-width, path-width, and cut-width (Wu et al. 2014). In this paper, we extend this line of research by exploring other graph width parameters: We obtain similar approximation hardness results under the SSEH for rank-width and maximum induced matching-width, while at the same time we show the approximation hardness of carving-width, clique-width, NLC-width, and boolean-width. We also give a simpler proof of the approximation hardness of tree-width, path-width, and cut-widththan that of Wu et al.

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 Strongly distance-balanced graphs and graph products

2009 ◽  
Vol 30 (5) ◽  
pp. 1048-1053 ◽  
Author(s):  
Kannan Balakrishnan ◽  
Manoj Changat ◽  
Iztok Peterin ◽  
Simon Špacapan ◽  
Primož Šparl ◽  
...  
Keyword(s):  
Graph Products ◽  
Balanced Graphs

On two conjectures on b-coloring of graph products

2017 ◽  
Vol 54 (1) ◽  
pp. 141-149
Author(s):  
S. Francis Raj ◽  
T. Kavaskar
Keyword(s):  
Graph Products

Tenacity of complete graph products and grids

Networks ◽  
1999 ◽  
Vol 34 (3) ◽  
pp. 192-196 ◽  
Author(s):  
S. A. Choudum ◽  
N. Priya
Keyword(s):  
Complete Graph ◽  
Graph Products

THE DIAMETER VARIABILITY OF THE CARTESIAN PRODUCT OF GRAPHS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
M. R. CHITHRA ◽  
A. VIJAYAKUMAR
Keyword(s):  
Interconnection Networks ◽  
Cartesian Product ◽  
Graph Products ◽  
Single Edge ◽  
Cartesian Product Of Graphs ◽  
Product Of Graphs

The diameter of a graph can be affected by the addition or deletion of edges. In this paper, we examine the Cartesian product of graphs whose diameter increases (decreases) by the deletion (addition) of a single edge. The problems of minimality and maximality of the Cartesian product of graphs with respect to its diameter are also solved. These problems are motivated by the fact that most of the interconnection networks are graph products and a good network must be hard to disrupt and the transmissions must remain connected even if some vertices or edges fail.

scholarly journals On the induced matching problem in hamiltonian bipartite graphs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yinglei Song
Keyword(s):  
Bipartite Graph ◽  
Parameterized Complexity ◽  
Bipartite Graphs ◽  
Matching Problem ◽  
Induced Matching ◽  
Subexponential Time ◽  
Maximum Induced Matching

Abstract In this paper, we study the parameterized complexity of the induced matching problem in hamiltonian bipartite graphs and the inapproximability of the maximum induced matching problem in hamiltonian bipartite graphs. We show that, given a hamiltonian bipartite graph, the induced matching problem is W[1]-hard and cannot be solved in time n o ⁢ ( k ) {n^{o(\sqrt{k})}} , where n is the number of vertices in the graph, unless the 3SAT problem can be solved in subexponential time. In addition, we show that unless NP = P {\operatorname{NP}=\operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of n 1 / 4 - ϵ {n^{1/4-\epsilon}} , where n is the number of vertices in the graph.

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