scholarly journals The induced matching and chain subgraph cover problems for convex bipartite graphs

2007 ◽  
Vol 381 (1-3) ◽  
pp. 260-265 ◽  
Author(s):  
Andreas Brandstädt ◽  
Elaine M. Eschen ◽  
R. Sritharan
Keyword(s):  
Bipartite Graphs ◽  
Induced Matching ◽  
Convex Bipartite Graphs

scholarly journals Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite Graphs

Algorithmica ◽  
2022 ◽  
Author(s):  
Boris Klemz ◽  
Günter Rote
Keyword(s):  
Bipartite Graph ◽  
Linear Time ◽  
Bipartite Graphs ◽  
Compact Representation ◽  
Maximum Cardinality ◽  
Induced Matching ◽  
Running Time ◽  
Induced Matchings ◽  
A Chain ◽  
Convex Bipartite Graphs

AbstractA bipartite graph $$G=(U,V,E)$$ G = ( U , V , E ) is convex if the vertices in V can be linearly ordered such that for each vertex $$u\in U$$ u ∈ U , the neighbors of u are consecutive in the ordering of V. An induced matchingH of G is a matching for which no edge of E connects endpoints of two different edges of H. We show that in a convex bipartite graph with n vertices and mweighted edges, an induced matching of maximum total weight can be computed in $$O(n+m)$$ O ( n + m ) time. An unweighted convex bipartite graph has a representation of size O(n) that records for each vertex $$u\in U$$ u ∈ U the first and last neighbor in the ordering of V. Given such a compact representation, we compute an induced matching of maximum cardinality in O(n) time. In convex bipartite graphs, maximum-cardinality induced matchings are dual to minimum chain covers. A chain cover is a covering of the edge set by chain subgraphs, that is, subgraphs that do not contain induced matchings of more than one edge. Given a compact representation, we compute a representation of a minimum chain cover in O(n) time. If no compact representation is given, the cover can be computed in $$O(n+m)$$ O ( n + m ) time. All of our algorithms achieve optimal linear running time for the respective problem and model, and they improve and generalize the previous results in several ways: The best algorithms for the unweighted problem versions had a running time of $$O(n^2)$$ O ( n 2 ) (Brandstädt et al. in Theor. Comput. Sci. 381(1–3):260–265, 2007. 10.1016/j.tcs.2007.04.006). The weighted case has not been considered before.

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.

Tree Convex Bipartite Graphs: $\mathcal{NP}$ -Complete Domination, Hamiltonicity and Treewidth

2014 ◽  
pp. 252-263 ◽  
Author(s):  
Chaoyi Wang ◽  
Hao Chen ◽  
Zihan Lei ◽  
Ziyang Tang ◽  
Tian Liu ◽  
...  
Keyword(s):  
Bipartite Graphs ◽  
Np Complete ◽  
Convex Bipartite Graphs

scholarly journals Hamiltonicity in convex bipartite graphs

2019 ◽  
Vol 11 (1) ◽  
pp. 40-52
Author(s):  
P. Kowsika ◽  
V. Divya ◽  
N. Sadagopan
Keyword(s):  
Bipartite Graphs ◽  
Convex Bipartite Graphs
Sign in / Sign up

Export Citation Format

Share Document