Weak Vertex Cover Problem in Certain Non-Regular Graphs

An Approximation Algorithm for Weighted Weak Vertex Cover Problem in Undirected Graphs

The problem of efficiently monitoring the network flow is regarded as the one to find out the minimum weighted weak vertex cover set for a given graph G = (V, E) with weight function w. In this paper, we show that a weak vertex cover set approximating a minimum one within 2− 2 ν(G) can be efficiently found in undirected graphs, and improve the previous work of approximation ratio within ln d + ...

Vertex Cover on 4 - regular Hyper - graphs is

Vertex-magic labeling of non-regular graphs

In this paper, we are studying vertex-magic total labelings (VMTLs) of simple graphs. By now much is known about methods for constructing VMTLs for regular graphs. Here we are studying non-regular graphs. We show how to construct labelings for several families of non-regular graphs, including graphs formed as the disjoint union of two other graphs already possessing VMTLs. We focus on condition...

On Total Vertex Cover Problem in Subcubic Graphs

A total vertex cover is a vertex cover whose induced subgraph consists of a set of connected components, each of which contains at least two vertices. The total vertex cover (TVC) problem ask for the total vertex cover with minimum cardinality. In this paper, we first show that the TVC problem is NP-complete for connected subcubic grid graphs of arbitrary large girth. Next, we show that the TVC...

Approximability of the vertex cover problem in power-law graphs

In this paper we construct an approximation algorithm for the Minimum Vertex Cover Problem (Min-VC) with an expected approximation ratio of 2 − ζ(β)−1− 1 2β 2βζ(β−1)ζ(β) for random Power Law Graphs (PLG) in the (α, β)-model of Aiello et. al.. We obtain this result by combining the Nemhauser and Trotter approach for Min-VC with a new deterministic rounding procedure which achieves an approximati...