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- W3131123246 abstract "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 <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>n</m:mi> <m:mrow> <m:mi>o</m:mi> <m:mo></m:mo> <m:mrow> <m:mo stretchy=false>(</m:mo> <m:msqrt> <m:mi>k</m:mi> </m:msqrt> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:mrow> </m:msup> </m:math> {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 <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi>NP</m:mi> <m:mo>=</m:mo> <m:mi mathvariant=normal>P</m:mi> </m:mrow> </m:math> {operatorname{NP}=operatorname{P}} , a maximum induced matching in a hamiltonian bipartite graph cannot be approximated within a ratio of <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>n</m:mi> <m:mrow> <m:mrow> <m:mn>1</m:mn> <m:mo>/</m:mo> <m:mn>4</m:mn> </m:mrow> <m:mo>-</m:mo> <m:mi>ϵ</m:mi> </m:mrow> </m:msup> </m:math> {n^{1/4-epsilon}} , where n is the number of vertices in the graph." @default.
- W3131123246 created "2021-03-01" @default.
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- W3131123246 date "2021-02-20" @default.
- W3131123246 modified "2023-10-16" @default.
- W3131123246 title "On the induced matching problem in hamiltonian bipartite graphs" @default.
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- W3131123246 doi "https://doi.org/10.1515/gmj-2021-2090" @default.
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