A 2-club is a graph of diameter at most two. In the decision version 2-Club Cluster Edge Deletion problem, an undirected G given along with integer k≥0 as parameter, and question whether can be transformed into disjoint union 2-clubs by deleting k edges. simple fixed-parameter algorithm solves problem in O⁎(3k), decade-old improved this running to O⁎(2.74k) time via more sophisticated case anal...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 26 November 2018Accepted: 06 2020Published online: 21 January 2021Keywordsimmersions, tree-cut width, graph modification problems, edge-deletion distance, kernelizationAMS Subject Headings05C70, 05C75, 05C83, 05C85Publication DataISSN (print): 0895-4801ISSN (online): 1095...

We present here 2-approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges deleted so that the remaining subgraph is bipartite complete. Several variants of the biclique prob...

The focus of this paper is two fold. Firstly, we present a logical approach to graph modification problems such as minimum node deletion, edge deletion, edge augmentation problems by expressing them as an expression in first order (FO) logic. As a consequence, it follows that these problems have constant factor polynomial-time approximation algorithms. In particular, node deletion/edge deletion...

For fixed integers r, l ≥ 0, a graph G is called an (r, l)-graph if the vertex set V (G) can be partitioned into r independent sets and l cliques. This brings us to the following natural parameterized questions: Vertex (r, l)-Partization and Edge (r, l)-Partization. An input to these problems consist of a graph G and a positive integer k and the objective is to decide whether there exists a set...

We look for graph polynomials which satisfy recurrence relations on three kinds of edge elimination: edge deletion, edge contraction and edge extraction, i.e., deletion of edges together with their end points. Like in the case of deletion and contraction only (J.G. Oxley and D.J.A. Welsh 1979), it turns out that there is a most general polynomial satisfying such recurrence relations, which we c...

In this paper the authors study the edge-integrity of graphs. Edge-integrity is a very useful measure of the vulnerability of a network, in particular a communication network, to disruption through the deletion of edges. A number of problems are examined, including some Nordhaus-Gaddum type results. Honest graphs, i.e. those which have the maximum possible edge-integrity, are also investigated....

Introduction In many diseases, the interface between diseased and healthy tissue contains a great deal of information. One example of this is the brain tumor oligodendroglioma. Tumors harbouring a specific genetic abnormality, 1p/19q co-deletion, have markedly different prognoses and responses to treatment than those that do not. Several magnetic resonance (MR) image features that are significa...

We characterize graphs of large enough order or large enough minimum degree which contain edge cuts whose deletion results in a graph with a specified number of large components. This generalizes and extends recent results due to Ou (Edge cuts leaving components of order at least m, Discrete Math. 305 (2005), 365-371) and Zhang and Yuan (A proof of an inequality concerning k-restricted edge con...