A faster FPT algorithm for 3-path vertex cover

A Faster FPT Algorithm for Bipartite Contraction

The Bipartite Contraction problem is to decide, given a graph G and a parameter k, whether we can can obtain a bipartite graph from G by at most k edge contractions. The fixed-parameter tractability of the problem was shown by Heggernes et al. [13], with an algorithm whose running time has double-exponential dependence on k. We present a new randomized FPT algorithm for the problem, which is bo...

A Faster FPT Algorithm and a Smaller Kernel for Block Graph Vertex Deletion

A graph G is called a block graph if each maximal 2-connected component of G is a clique. In this paper we study the Block Graph Vertex Deletion from the perspective of fixed parameter tractable (FPT) and kernelization algorithm. In particular, an input to Block Graph Vertex Deletion consists of a graph G and a positive integer k and the objective to check whether there exists a subset S ⊆ V (G...

Faster Computation of the Maximum Dissociation Set and Minimum 3-Path Vertex Cover in Graphs

Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

A 3-path vertex cover in a graph is a vertex subset C such that every path of three vertices contains at least one vertex from C. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most k. In this paper, we give a kernel of 5k vertices and an O(1.7485)-time polynomial-space algorithm for this problem, both new results improve previous known b...

A simple local 3-approximation algorithm for vertex cover

Given a graph G = (V , E), a subset of nodes C ⊆ V is a vertex cover if each edge {u, v} ∈ E has u ∈ C or v ∈ C . In this work, we present a constant-time distributed algorithm for finding a factor 3 approximation for minimum vertex cover in bounded-degree graphs. A distributed algorithm that runs in constant time (constant number of synchronous communication rounds) is called a local algorithm...