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.
An Algorithm for Computing a Gröbner Basis of a Polynomial Ideal over a Ring with Zero Divisors
