# On the induced matching problem in hamiltonian bipartite graphs

On the induced matching problem in hamiltonian bipartite graphs AbstractIn this paper, we study the parameterized complexityof the induced matching problem in hamiltonian bipartite graphs and the inapproximability ofthe 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 no⁢(k){n^{o(\sqrt{k})}},where n is the number of vertices in the graph, unless the 3SATproblem 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 n1/4-ϵ{n^{1/4-\epsilon}},where n is the number of vertices in the graph. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

# On the induced matching problem in hamiltonian bipartite graphs

, Volume 28 (6): 14 – Dec 1, 2021
14 pages

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Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2021-2090
Publisher site
See Article on Publisher Site

### Abstract

AbstractIn this paper, we study the parameterized complexityof the induced matching problem in hamiltonian bipartite graphs and the inapproximability ofthe 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 no⁢(k){n^{o(\sqrt{k})}},where n is the number of vertices in the graph, unless the 3SATproblem 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 n1/4-ϵ{n^{1/4-\epsilon}},where n is the number of vertices in the graph.

### Journal

Georgian Mathematical Journalde Gruyter

Published: Dec 1, 2021

Keywords: Induced matching; hamiltonian bipartite graphs; parameterized complexity; inapproximability; 68Q17

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