DeepAI AI Chat
Log In Sign Up

Tractability of Konig Edge Deletion Problems

by   Diptapriyo Majumdar, et al.
The Institute of Mathematical Sciences, Chennai

A graph is said to be a Konig graph if the size of its maximum matching is equal to the size of its minimum vertex cover. The Konig Edge Deletion problem asks if in a given graph there exists a set of at most k edges whose deletion results in a Konig graph. While the vertex version of the problem (Konig vertex deletion) has been shown to be fixed-parameter tractable more than a decade ago, the fixed-parameter-tractability of the Konig Edge Deletion problem has been open since then, and has been conjectured to be W[1]-hard in several papers. In this paper, we settle the conjecture by proving it W[1]-hard. We prove that a variant of this problem, where we are given a graph G and a maximum matching M and we want a k-sized Konig edge deletion set that is disjoint from M, is fixed-parameter-tractable.


page 1

page 2

page 3

page 4


Structural Parameterizations of the Biclique-Free Vertex Deletion Problem

In this work, we study the Biclique-Free Vertex Deletion problem: Given ...

Edge Deletion to Restrict the Size of an Epidemic

Given a graph G=(V,E), a set ℱ of forbidden subgraphs, we study ℱ-Free E...

Efficient Network Analysis Under Single Link Deletion

The problem of worst case edge deletion from a network is considered. Su...

On Bayesian Network Approximation by Edge Deletion

We consider the problem of deleting edges from a Bayesian network for th...

Parameterized algorithms for Eccentricity Shortest Path Problem

Given an undirected graph G=(V,E) and an integer ℓ, the Eccentricity Sho...

An Improved Fixed-Parameter Algorithm for 2-Club Cluster Edge Deletion

A 2-club is a graph of diameter at most two. In the decision version of ...

Deletion to Induced Matching

In the DELETION TO INDUCED MATCHING problem, we are given a graph G on n...