scholarly journals On Maximum Induced Matching Numbers of Special Grids

2018 ◽  
Author(s):  
Tayo Charles Adefokun ◽  
Deborah Olayide Ajayi
Keyword(s):  
Induced Matching ◽  
Maximum Induced Matching ◽  
Special Grids

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.

scholarly journals Maximum Induced Matching Algorithms via Vertex Ordering Characterizations

Algorithmica ◽  
2019 ◽  
Author(s):  
Michel Habib ◽  
Lalla Mouatadid
Keyword(s):  
Induced Matching ◽  
Vertex Ordering ◽  
Maximum Induced Matching

scholarly journals Finding a maximum induced matching in weakly chordal graphs

2003 ◽  
Vol 266 (1-3) ◽  
pp. 133-142 ◽  
Author(s):  
Kathie Cameron ◽  
R. Sritharan ◽  
Yingwen Tang
Keyword(s):  
Chordal Graphs ◽  
Induced Matching ◽  
Maximum Induced Matching

scholarly journals The graphs with maximum induced matching and maximum matching the same size

2005 ◽  
Vol 299 (1-3) ◽  
pp. 49-55 ◽  
Author(s):  
Kathie Cameron ◽  
Tracy Walker
Keyword(s):  
Maximum Matching ◽  
Induced Matching ◽  
Maximum Induced Matching

scholarly journals Exact algorithms for Maximum Induced Matching

2017 ◽  
Vol 256 ◽  
pp. 196-211 ◽  
Author(s):  
Mingyu Xiao ◽  
Huan Tan
Keyword(s):  
Exact Algorithms ◽  
Induced Matching ◽  
Maximum Induced Matching

scholarly journals Latest Algorithms on Particular Graph Classes

2020 ◽  
pp. 21-35
Author(s):  
Phan Thuan DO ◽  
Ba Thai PHAM ◽  
Viet Cuong THAN
Keyword(s):  
Optimization Problems ◽  
Linear Time ◽  
Maximum Clique ◽  
Independent Set ◽  
Maximum Independent Set ◽  
Np Hard ◽  
Induced Matching ◽  
Graph Classes ◽  
Maximum Induced Matching ◽  
Circular Arc Graphs

Many optimization problems such as Maximum Independent Set, Maximum Clique, Minimum Clique Cover and Maximum Induced Matching are NP-hard on general graphs. However, they could be solved in polynomial time when restricted to some particular graph classes such as comparability and co-comparability graph classes. In this paper, we summarize the latest algorithms solving some classical NP-hard problems on some graph classes over the years. Moreover, we apply the -redundant technique to obtain linear time O(j j) algorithms which find a Maximum Induced Matching on interval and circular-arc graphs. Inspired of these results, we have proposed some competitive programming problems for some programming contests in Vietnam in recent years.

scholarly journals Efficient Algorithms for Maximum Induced Matching Problem in Permutation and Trapezoid Graphs

2021 ◽  
Vol 182 (3) ◽  
pp. 257-283
Author(s):  
Viet Dung Nguyen ◽  
Ba Thai Pham ◽  
Phan Thuan Do
Keyword(s):  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Matching Problem ◽  
Induced Matching ◽  
Graph Classes ◽  
Permutation Models ◽  
Maximum Induced Matching ◽  
Sweep Line ◽  
Trapezoid Graphs ◽  
Better Than

We first design an 𝒪(n2) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to 𝒪(m+n). Consequently, we extend this result to give an 𝒪(m+n) algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and 𝒪(n2) time, respectively. Our results are far better than the best known 𝒪(mn) algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.

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