Vertex Cover
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Recent papers in Vertex Cover
A Minimum Vertex Cover is the smallest set of vertices whose removal completely disconnects a graph. In this paper, we perform experiments on a number of graphs from standard complex networks databases addressing the problem of finding a... more
We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We... more
Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I. It is shown that the minimal generators of Rs(I) are in one to one correspondence... more
We give a new proof of K\"onig's theorem and generalize the Gallai-Edmonds decomposition to balanced hypergraphs in two different ways. Based on our decompositions we give two new characterizations of balanced hypergraphs and... more
We explore opportunities for parameterising constant factor approximation algorithms for vertex cover. We provide a simple algorithm that works on any approximation ratio of the form \frac 2l+1l+1\frac {2l+1}{l+1} and has complexity that... more
The remarkable discovery of many large-scale real networks is the power-law distribution in degree sequence: the number of vertices with degree i is proportional to i− β for some constant β> 1. A lot of researchers believe that it may... more
A function � : V ! {1,...,k} is a broadcast coloring of order k if �(u) = �(v) implies that the distance between u and v is more than �(u). The minimum order of a broadcast coloring is called the broadcast chromatic number of G, and is... more
Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multiple-interval graphs by considering three... more
The minimum vertex cover (MVC) and maximum independent set (MIS) problems are to be determined in terms of a graph of the small set of vertices, which cover all the edges, and a large set of vertices, no two of which are adjacent. MVC and... more
The MINIMUM 2SAT-DELETION problem is to delete the minimum number of clauses in a 2SAT instance to make it satisfiable. It is one of the prototypes in the approximability hierarchy of minimization problems Khanna et al. [Constraint... more
An odd graceful labeling of a graph G = (V ,E ) is a function f :V (G)® {0,1,2, . . .2 E(G) −1}such that |f (u)−f (v)| is odd value less than or equal to 2 E(G) −1 for any u ,v ÎV (G) . In spite of the large number of papers published on... more
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0 or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved that, the graphs which are... more
A variety of efficient kernelization strategies for the classic vertex cover problem are developed, implemented and compared experimentally. A new technique, termed crown reduction, is introduced and analyzed. Applications to... more
A set D of vertices of a graph G is a dominating set if every vertex in V \ D is adjacent to some vertex in D.
In this paper, we provide a constructive characterization of trees with unique minimum dominating set.
In this paper, we provide a constructive characterization of trees with unique minimum dominating set.
Wireless sensor and actor networks (WSANs) consist of powerful actors and resource constraint sensors that are linked together in wireless networks. They mostly rely on actors to make proper decisions and perform desired coordination to... more
Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the given graph can be covered with at most k bicliques (complete bipartite subgraphs); the biclique vertex-cover problem asks whether the vertex-set... more
Broadcasting in processor networks means disseminating a single piece of information, which is originally known only at some nodes, to all members of the network. The goal is to inform everybody using as few rounds as possible, that is to... more
In this paper we present a detailed study of the hitting set (HS) problem. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge... more
Abstract: The framework of Bodlaender et al.(ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However,... more