Article history: Received 21 October 2013 Received in revised form 30 September 2014 Accepted 21 October 2014 Available online 28 October 2014 Communicated by G. Ausiello

It is shown that when a special vertex stretching is applied to a graph, the cochordal cover number of the graph increases exactly by one, as it happens to its induced matching number and (Castelnuovo-Mumford) regularity. As a consequence, it is shown that the induced matching number and cochordal cover number of a special vertex stretching of a graph G are equal provided G is well-covered bipa...

In a recent paper Soleimanfallah and Yeo proposed a kernelization algorithm for Vertex Cover which, for any xed constant c, produces a kernel of order 2k−c in polynomial time. In this paper we show how their techniques can be extended to improve the produced kernel to order 2k − c log k, for any xed constant c.

Cardinality Maximum Flow Network Interdiction Problem (CMFNIP) is known to be strongly NP-hard problem in the literature. A particular case of CMFNIP has been shown to have reduction from clique problem. In the present work,an effort is being made to solve this particular case of CMFNIP in polynomial time. Direct implication of this solution is that the clique problem gets solved in polynomial ...

The pair (G, D) consisting of a planar graph G V, E) with n vertices together with a subset of d special vertices D V is called k-planar if there is an embedding of G in the plane so that at most k faces of G are required to cover all of the vertices in D. Checking 1-planarity can be done in linear-time since it reduces to a problem of checking planarity of a related graph. We present an algori...

Kernelization is a powerful tool to obtain fixed-parameter tractable algorithms. Recent breakthroughs show that many graph problems admit small polynomial kernels when restricted to sparse graph classes such as planar graphs, bounded-genus graphs or H-minor-free graphs. We consider the intersection graphs of (unit) disks in the plane, which can be arbitrarily dense but do exhibit some geometric...

We propose the “Competing Salesmen Problem” (CSP), a 2-player competitive version of the classical Traveling Salesman Problem. This problem arises when considering two competing salesmen instead of just one. The concern for a shortest tour is replaced by the necessity to reach any of the customers before the opponent does. In particular, we consider the situation where players take turns, movin...

For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-ha...

Linear and semidefinite programming are highly successful approaches for obtaining good approximations for NP-hard optimization problems. For example, breakthrough approximation algorithms for MAX CUT and SPARSEST CUT use semidefinite programming. Perhaps the most prominent NP-hard problem whose exact approximation factor is still unresolved is VERTEX COVER. PCP-based techniques of Dinur and Sa...

We introduce a surprisingly simple technique to design and analyze algorithms based on search trees, that significantly improves many existing results in the area of exact algorithms. The technique is based on measuring the progress of Branch & Bound algorithms by making use of a combinatorial relation between the average and maximum dual degrees of a graph. By dual degree of a vertex, we mean ...