This paper proves that the problem of finding connected vertex cover in a 2-connected planar graph ( CVC-2 ) with maximum degree 4 is NP-complete. The motivation for proving this result is to give a shorter and simpler proof of NP-Completeness of TRA-MLC (the Top Right Access point ...
What is known about Vertex Cover Kernelization? We are pleased to dedicate this survey on kernelization of the Vertex Cover problem, to Professor Juraj Hromkovi\v{c} on the occasion of his 60th birthday. The Vertex Cover problem is often referred to as the Drosophila of parameterized ...
摘要: Starting from the vertex cover problem, this paper obtains a more particular NP-complete problem (comparing with the feedback vertex set problem) and its counterpart in finite automata theory关键词: Theoretical or Mathematical/ finite automata set theory/ vertex cover NP-complete feedback ...
When can $t$ terminal pairs in an $m imes n$ grid be connected by $t$ vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch's 1975 proof without the ``...
Subset Correspondence, otherwise called the "Subset Total" issue, is an exemplary NP-complete computational issue. Given a bunch of numbers and an objective worth, the undertaking is to decide if there exists a subset of the numbers whose total is equivalent to the objective worth. The issue'...
The answer to NP-complete problems remains unknown. It's worth noting that when single NP-complete issue is able to be answered in polynomial time, then all others may be resolved as well. Dense Subgraph A dense subgraph is one that has numerous edges for each vertex in the theory of ...
LibMVC is a collection of fast iterative minimum vertex cover solvers. Currently the following algorithms are implemented: NuMVC FastVC The solvers take a graph in DIMACS format as input and calculate the minimum vertex cover / independent set. During the calculation, approximations are provided. ...
A vertex cover of a complete bipartite graph must use all of one part. Since have all the neighbors in these two sets, we can remove one of that is not in the right part and decrease the size of the vertex cover. Thus a minimum vertex cover of size yields an antichain of size . ...
Identify which of these problems are NP-complete and which can be exactly solved using a polynomial time algorithm. a. Finding the vertex cover in a line graph. b. Finding the maximum clique in a tree How many bit strings of length 10 have a) exactly...
In this work we additionally consider the three classical \textsf {NP}-complete problems Minimum Dominating Set(MDS), Maximum Independent Set(MIS) and Minimum Vertex Cover(MVC) on PLB-U networks. For the first two problems, positive results are already known for (\alpha , \beta )-Power Law...