7,902 research outputs found
Vertex Deletion into Bipartite Permutation Graphs
A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines ?? and ??, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n-vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP-complete by the classical result of Lewis and Yannakakis [John M. Lewis and Mihalis Yannakakis, 1980].
We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time f(k)n^O(1), and also give a polynomial-time 9-approximation algorithm
Vertex deletion into bipartite permutation graphs
A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines \u1d4c1₁ and \u1d4c1₂, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n-vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP-complete by the classical result of Lewis and Yannakakis [John M. Lewis and Mihalis Yannakakis, 1980]. We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time f(k)n^O(1), and also give a polynomial-time 9-approximation algorithm
Vertex deletion into bipartite permutation graphs
A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines and , one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n-vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP-complete by the classical result of Lewis and Yannakakis [20]. We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time , and also give a polynomial-time 9-approximation algorithm
Vertex deletion into bipartite permutation graphs
A permutation graph can be defined as an intersection graph of segments whose
endpoints lie on two parallel lines and , one on each. A bipartite
permutation graph is a permutation graph which is bipartite. In this paper we
study the parameterized complexity of the bipartite permutation vertex deletion
problem, which asks, for a given n-vertex graph, whether we can remove at most
k vertices to obtain a bipartite permutation graph. This problem is NP-complete
by the classical result of Lewis and Yannakakis. We analyze the structure of
the so-called almost bipartite permutation graphs which may contain holes
(large induced cycles) in contrast to bipartite permutation graphs. We exploit
the structural properties of the shortest hole in a such graph. We use it to
obtain an algorithm for the bipartite permutation vertex deletion problem with
running time , and also give a polynomial-time 9-approximation
algorithm.Comment: Extended abstract accepted to International Symposium on
Parameterized and Exact Computation (IPEC'20
A polynomial kernel for vertex deletion into bipartite permutation graphs
A permutation graph can be defined as an intersection graph of segments whose
endpoints lie on two parallel lines and , one on each. A
bipartite permutation graph is a permutation graph which is bipartite.
In the the bipartite permutation vertex deletion problem we ask for a given
-vertex graph, whether we can remove at most vertices to obtain a
bipartite permutation graph. This problem is NP-complete but it does admit an
FPT algorithm parameterized by .
In this paper we study the kernelization of this problem and show that it
admits a polynomial kernel with vertices
Calculation of the Number of all Pairs of Disjoint S-permutation Matrices
The concept of S-permutation matrix is considered. A general formula for
counting all disjoint pairs of S-permutation matrices as a
function of the positive integer is formulated and proven in this paper. To
do that, the graph theory techniques have been used. It has been shown that to
count the number of disjoint pairs of S-permutation matrices,
it is sufficient to obtain some numerical characteristics of all
bipartite graphs.Comment: arXiv admin note: text overlap with arXiv:1211.162
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