A list heuristic for vertex cover

Improved Bounds on the List Decreasing Heuristic for the Vertex Cover Problem

The list decreasing heuristic for the vertex cover problem is an online vertex covering algorithm. An upper bound ∆ /2+3/2 had been proposed on the approximation ratio for it, and a graph had also been given to reach a lower bound of ∆ /2+1/2. In this paper, we refine the techniques of previous researchers, and construct a new type of graphs which can enhance the lower bound to ∆ /2+1 , and all...

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...

An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem in Graph Theory

The connected vertex cover (CVC) problem is a variant of the vertex cover problem, 1 which has many important applications, such as wireless network design, routing and wavelength 2 assignment problem, etc. A good algorithm for the problem can help us improve engineering 3 efficiency, cost savings and resources in industrial applications. In this work, we present an efficient 4 algorithm GRASP-...

An Evolutionary Heuristic for the Minimum Vertex Cover Problem

On list vertex 2-arboricity of toroidal graphs without cycles of specific length

The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph‎. ‎A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$‎, ‎one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...