Vertex deletion into bipartite permutation graphs

10/22/2020
by   Łukasz Bożyk, et al.
0

A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines l_1 and l_2, 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 O(9^k· n^9), and also give a polynomial-time 9-approximation algorithm.

READ FULL TEXT

page 1

page 2

page 3

page 4

11/27/2021

A polynomial kernel for vertex deletion into bipartite permutation graphs

A permutation graph can be defined as an intersection graph of segments ...
11/17/2021

Roman Domination in Convex Bipartite Graphs

In the Roman domination problem, an undirected simple graph G(V,E) is gi...
03/30/2021

Applications of Common Information to Computing Functions

We design a low complexity distributed compression scheme for computing ...
12/20/2018

A spectral method for bipartizing a network and detecting a large anti-community

Relations between discrete quantities such as people, genes, or streets ...
10/04/2018

The Four Point Permutation Test for Latent Block Structure in Incidence Matrices

Transactional data may be represented as a bipartite graph G:=(L ∪ R, E)...
03/26/2020

A Blind Permutation Similarity Algorithm

This paper introduces a polynomial blind algorithm that determines when ...
09/24/2022

Compressing bipartite graphs with a dual reordering scheme

In order to manage massive graphs in practice, it is often necessary to ...