On approximating minimum vertex cover for graphs with perfect matching

On Approximating Minimum Vertex Cover for Graphs with Perfect Matching

It has been a challenging open problem whether there is a polynomial time approximation algorithm for the Vertex Cover problem whose approximation ratio is bounded by a constant less than 2. In this paper, we study the Vertex Cover problem on graphs with perfect matching (shortly, VC-PM). We show that if the VC-PM problem has a polynomial time approximation algorithm with approximation ratio bo...

On Approximating Minimum Vertex Cover for Graphs with Perfe t Mat hing

Critical Graphs for Minimum Vertex Cover

An α-critical graph is an instance where the deletion of any element would decrease some graph’s measure α. Such instances have shown to be interesting objects of study for deepen the understanding of optimization problems. This work explores critical graphs in the context of the Minimum-Vertex-Cover problem. We demonstrate their potential for the generation of larger graphs with hidden a prior...

Approximated Vertex Cover for Graphs with Perfect Matchings

Chen and Kanj considered the V C problem for graphs with perfect matchings (VC-PM). They showed that: (i) There is a reduction from general V C to VC-PM, which guarantees that if one can achieve an approximation factor of less than two for VC-PM, then one can do so for general V C as well. (ii) There is an algorithm for VC-PM whose approximation factor is given as 1.0...

Minimum Vertex Cover in Rectangle Graphs

We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R1 \ R2 is connected for every pair of rectangles R1, R2 ∈ R. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor of (1.5 + ...