A faster FPT algorithm for 3-path vertex cover

Approximation algorithms for minimum (weight) connected k -path vertex cover

An FPT algorithm for the vertex cover P 4 problem

http://www.cs.technion.ac.il/~reuven/SAVE/OTHERS/connected-k-subgraph.pdf

Approximation algorithm for the minimum weight connected k-subgraph cover problem☆

Approximation algorithms for minimum weight connected 3-path vertex cover

A subset F of vertices of a graph G is called a vertex cover Pk set if every path of order k in G contains at least one vertex from F. Denote by ψk(G) the minimum cardinality of a vertex cover Pk set in G. The vertex cover Pk (VCPk) problem is to find a minimum vertex cover Pk set. It is easy to see that the VCP2 problem corresponds to the well-known vertex cover problem. In this paper, we restrict our attention to the VCP4 problem in cubic graphs. The paper proves that the VCP4 problem is NP-hard for cubic graphs. Further, we give sharp lower and upper bounds on ψ4(G) for cubic graphs and propose a 2-approximation algorithm for the VCP4 problem in cubic graphs.

Jianhua Tu

Papers

A 2-approximation algorithm for the vertex cover P4 problem in cubic graphs