An Improved Fixed-Parameter Algorithm for Vertex Cover

Improvement on vertex cover for low-degree graphs

The Vertex Cover problem (given a graph G and an integer k, decide if G has a vertex cover of k vertices) is one of the six “basic” NP-complete problems according to Garey and Johnson [7]. It is fixed-parameter tractable in terms of Downey and Fellows [5], that is, it can be solved in time O(f(k)n), where f is a function of the parameter k but independent of the input length n and c is a consta...

Exact Algorithms for Generalizations of Vertex Cover

The NP-complete Vertex Cover problem has been intensively studied in the field of parameterized complexity theory. However, there exists only little work concerning important generalizations of Vertex Cover like Partial Vertex Cover, Connected Vertex Cover, and Capacitated Vertex Cover which are of high interest in theory as well as in real-world applications. So far research was mainly focused...

Solving Minimum Vertex Cover : A Fast Fixed - Parameter - Tra table Algorithm for Pro t Cover ?

Parameterized Complexity of the List Coloring Reconfiguration Problem with Graph Parameters

Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even ...

Raising The Bar For Vertex Cover: Fixed-parameter Tractability Above A Higher Guarantee

The standard parameterization of the VERTEX COVER problem (Given an undirected graph G and k ∈ N as input, does G have a vertex cover of size at most k?) has the solution size k as the parameter. The following more challenging parameterization of VERTEX COVER stems from the observation that the size MM of a maximum matching of G lower-bounds the size of any vertex cover of G: Does G have a vert...